{"id":375,"date":"2018-04-17T02:37:10","date_gmt":"2018-04-17T02:37:10","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/?post_type=chapter&#038;p=375"},"modified":"2024-04-26T22:09:06","modified_gmt":"2024-04-26T22:09:06","slug":"graphing-points","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/chapter\/graphing-points\/","title":{"raw":"Graphing Points on a Coordinate Plane","rendered":"Graphing Points on a Coordinate Plane"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning outcome<\/h3>\r\n<ul>\r\n \t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Graph points (ordered pairs) on a coordinate plane&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:13185,&quot;3&quot;:[null,0],&quot;10&quot;:2,&quot;11&quot;:4,&quot;12&quot;:0,&quot;15&quot;:&quot;Calibri&quot;,&quot;16&quot;:10}\">Graph points (ordered pairs) on a coordinate plane<\/span><\/li>\r\n<\/ul>\r\n<\/div>\r\n<p data-type=\"title\">Many maps, such as the Campus Map shown below, use a grid system to identify locations. Do you see the numbers [latex]1,2,3[\/latex], and [latex]4[\/latex] across the top and bottom of the map and the letters A, B, C, and D along the sides? Every location on the map can be identified by a number and a letter.<\/p>\r\n<p data-type=\"title\">For example, the Student Center is in section 2B. It is located in the grid section above the number [latex]2[\/latex] and next to the letter B. In which grid section is the Stadium? The Stadium is in section 4D.<\/p>\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224708\/CNX_BMath_Figure_11_01_001.png\" alt=\"The figure shows a labeled grid representing the Campus Map. The columns are labeled 1 through 4 and the rows are labeled A through D. At position A-1 is the title Parking Garage. At position A-4 is a rectangle labeled Residence Halls. At position B-2 is a rectangle labeled Student Center. At position B-3 is a rectangle labeled Engineering Building. At position C-1 is a rectangle labeled Taylor Hall. At position C-2 is a rectangle labeled Library. At position C-4 is a rectangle labeled Tiger Field. At position D-4 is a rectangle labeled Stadium.\" data-media-type=\"image\/png\" \/>\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nUse the map above.\r\n<ol id=\"eip-id1164754238718\" class=\"circled\" data-number-style=\"arabic\">\r\n \t<li>Find the grid section of the Residence Halls.<\/li>\r\n \t<li>What is located in grid section 4C?<\/li>\r\n<\/ol>\r\nSolution\r\n<ol id=\"eip-id1164753925474\" class=\"circled\" data-number-style=\"arabic\">\r\n \t<li>Read the number below the Residence Halls, [latex]4[\/latex], and the letter to the side, A. So the Residence Halls are in grid section 4A.<\/li>\r\n \t<li>Find [latex]4[\/latex] across the bottom of the map and C along the side. Look below the [latex]4[\/latex] and next to the C. Tiger Field is in grid section 4C.<\/li>\r\n<\/ol>\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146887[\/ohm_question]\r\n\r\n[ohm_question]146888[\/ohm_question]\r\n\r\n<\/div>\r\nJust as maps use a grid system to identify locations, a grid system is used in algebra to show a relationship between two variables in a rectangular coordinate system. To create a rectangular coordinate system, start with a horizontal number line. Show both positive and negative numbers as you did before, using a convenient scale unit. This horizontal number line is called the [latex]x[\/latex]-axis.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224711\/CNX_BMath_Figure_11_01_026_img.png\" alt=\"The figure shows a number line with integer values labeled from -5 to 5.\" data-media-type=\"image\/png\" \/>\r\nNow, make a vertical number line passing through the [latex]x[\/latex]-axis at [latex]0[\/latex]. Put the positive numbers above [latex]0[\/latex] and the negative numbers below [latex]0[\/latex]. See the image below. This vertical line is called the[latex]y[\/latex]-axis.\r\n\r\nVertical grid lines pass through the integers marked on the [latex]x[\/latex]-axis. Horizontal grid lines pass through the integers marked on the [latex]y[\/latex]-axis]. The resulting grid is the rectangular coordinate system.\r\n\r\nThe rectangular coordinate system is also called the [latex]x\\text{-}y[\/latex] plane, the coordinate plane, or the Cartesian coordinate system (since it was developed by a mathematician named Ren\u00e9 Descartes.)\r\n<div class=\"textbox shaded\">\r\n<h3>The rectangular coordinate system<\/h3>\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224713\/CNX_BMath_Figure_11_01_002.png\" alt=\"The graph shows the x y-coordinate plane. The x and y-axis each run from -7 to 7. An arrow points to the horizontal axis with the label x-axis. An arrow points to the vertical axis with the label y-axis.\" width=\"367\" height=\"372\" data-media-type=\"image\/png\" \/>\r\n\r\n<\/div>\r\nThe [latex]x[\/latex]-axis] and the\u00a0[latex]y[\/latex]-axis form the rectangular coordinate system. These axes divide a plane into four areas, called quadrants. The quadrants are identified by Roman numerals, beginning on the upper right and proceeding counterclockwise. See the image below.\r\n<div class=\"textbox shaded\">\r\n<h3>The four quadrants of the rectangular coordinate system<\/h3>\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224716\/CNX_BMath_Figure_11_01_003.png\" alt=\"The graph shows the x y-coordinate plane. The x and y-axis each run from -7 to 7. The top-right portion of the plane is labeled I. The top-left portion of the place is labeled II. The bottom-left portion of the table is labeled III. The bottom-right portion of the table is labeled IV.\" width=\"345\" height=\"354\" data-media-type=\"image\/png\" \/>\r\n\r\n<\/div>\r\nIn the rectangular coordinate system, every point is represented by an ordered pair. The first number in the ordered pair is the <em data-effect=\"italics\">x<\/em>-coordinate of the point, and the second number is the <em data-effect=\"italics\">y<\/em>-coordinate of the point.\r\n<div class=\"textbox shaded\">\r\n<h3>Ordered Pair<\/h3>\r\nAn ordered pair, [latex]\\left(x,y\\right)[\/latex] gives the coordinates of a point in a rectangular coordinate system.\r\n\r\n[latex]\\begin{array}{c}\\text{The first number is the }x\\text{-coordinate}.\\hfill \\\\ \\text{The second number is the }y\\text{-coordinate}.\\hfill \\end{array}[\/latex]\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224718\/CNX_BMath_Figure_11_01_027_img.png\" alt=\"The ordered pair x y is labeled with the first coordinate x labeled as x-coordinate and the second coordinate y labeled y-coordinate.\" width=\"226\" height=\"68\" data-media-type=\"image\/png\" \/>\r\n\r\n<\/div>\r\nSo how do the coordinates of a point help you locate a point on the [latex]x\\text{-}y[\/latex] plane?\r\n\r\nLet\u2019s try locating the point [latex]\\left(2,5\\right)[\/latex] . In this ordered pair, the [latex]x[\/latex] -coordinate is [latex]2[\/latex] and the [latex]y[\/latex] -coordinate is [latex]5[\/latex] .\r\n\r\nWe start by locating the [latex]x[\/latex] value, [latex]2[\/latex], on the [latex]x\\text{-axis.}[\/latex] Then we lightly sketch a vertical line through [latex]x=2[\/latex], as shown in the image below.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224719\/CNX_BMath_Figure_11_01_004.png\" alt=\"The graph shows the x y-coordinate plane. The x and y-axis each run from -6 to 6. There is a vertical dotted line passing through 2 on the x-axis.\" data-media-type=\"image\/png\" \/>\r\nNow we locate the [latex]y[\/latex] value, [latex]5[\/latex], on the [latex]y[\/latex] -axis and sketch a horizontal line through [latex]y=5[\/latex] . The point where these two lines meet is the point with coordinates [latex]\\left(2,5\\right)[\/latex]. We plot the point there, as shown in the image below.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224721\/CNX_BMath_Figure_11_01_005.png\" alt=\"The graph shows the x y-coordinate plane. The x and y-axis each run from -6 to 6. The point (2, 5) is labeled, and dashed vertical and horizontal lines run through this point.\" width=\"301\" height=\"308\" data-media-type=\"image\/png\" \/>\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nPlot [latex]\\left(1,3\\right)[\/latex] and [latex]\\left(3,1\\right)[\/latex] in the same rectangular coordinate system.\r\n[reveal-answer q=\"501893\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"501893\"]\r\n\r\nSolution\r\nThe coordinate values are the same for both points, but the [latex]x[\/latex] and [latex]y[\/latex] values are reversed. Let\u2019s begin with point [latex]\\left(1,3\\right)[\/latex]. The [latex]x\\text{-coordinate}[\/latex] is [latex]1[\/latex] so find [latex]1[\/latex] on the [latex]x\\text{-axis}[\/latex] and sketch a vertical line through [latex]x=1[\/latex]. The [latex]y\\text{-coordinate}[\/latex] is [latex]3[\/latex] so we find [latex]3[\/latex] on the [latex]y\\text{-axis}[\/latex] and sketch a horizontal line through [latex]y=3[\/latex]. Where the two lines meet, we plot the point [latex]\\left(1,3\\right)[\/latex].\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224723\/CNX_BMath_Figure_11_01_006_img.png\" alt=\"The graph shows the x y-coordinate plane. The x and y-axis each run from -6 to 6. The point (1, 3) is labeled, and dashed vertical and horizontal lines run through this point.\" width=\"308\" height=\"316\" data-media-type=\"image\/png\" \/>\r\nTo plot the point [latex]\\left(3,1\\right)[\/latex], we start by locating [latex]3[\/latex] on the [latex]x\\text{-axis}[\/latex] and sketch a vertical line through [latex]x=3[\/latex]. Then we find [latex]1[\/latex] on the [latex]y\\text{-axis}[\/latex] and sketch a horizontal line through [latex]y=1[\/latex]. Where the two lines meet, we plot the point [latex]\\left(3,1\\right)[\/latex].\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224725\/CNX_BMath_Figure_11_01_007_img.png\" alt=\"The graph shows the x y-coordinate plane. The x and y-axis each run from -6 to 6. The point (3, 1) is labeled, and dashed vertical and horizontal lines run through this point. The point (1, 3) is also labeled.\" width=\"316\" height=\"323\" data-media-type=\"image\/png\" \/>\r\nNotice that the order of the coordinates does matter, so, [latex]\\left(1,3\\right)[\/latex] is not the same point as [latex]\\left(3,1\\right)[\/latex].\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146882[\/ohm_question]\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Exercises<\/h3>\r\nPlot each point in the rectangular coordinate system and identify the quadrant in which the point is located:\r\n\r\n1. [latex]\\left(-1,3\\right)[\/latex]\r\n2. [latex]\\left(-3,-4\\right)[\/latex]\r\n3. [latex]\\left(2,-3\\right)[\/latex]\r\n4. [latex]\\left(3,{\\Large\\frac{5}{2}}\\right)[\/latex]\r\n[reveal-answer q=\"933080\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"933080\"]\r\n\r\nSolution\r\nThe first number of the coordinate pair is the [latex]x\\text{-coordinate}[\/latex], and the second number is the [latex]y\\text{-coordinate}[\/latex].\r\n1. Since [latex]x=-1,y=3[\/latex], the point [latex]\\left(-1,3\\right)[\/latex] is in Quadrant II.\r\n2. Since [latex]x=-3,y=-4[\/latex], the point [latex]\\left(-3,-4\\right)[\/latex] is in Quadrant III.\r\n3. Since [latex]x=2,y=-1[\/latex], the point [latex]\\left(2,-1\\right)[\/latex] is in Quadrant lV.\r\n4. Since [latex]x=3,y={\\Large\\frac{5}{2}}[\/latex], the point [latex]\\left(3,{\\Large\\frac{5}{2}}\\right)[\/latex] is in Quadrant I. It may be helpful to write [latex]{\\Large\\frac{5}{2}}[\/latex] as the mixed number, [latex]2{\\Large\\frac{1}{2}}[\/latex], or decimal, [latex]2.5[\/latex]. Then we know that the point is halfway between [latex]2[\/latex] and [latex]3[\/latex] on the [latex]y\\text{-axis}[\/latex].\r\n\r\n<img class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224731\/CNX_BMath_Figure_11_01_010.png\" alt=\"The graph shows the x y-coordinate plane. The x and y-axis each run from -7 to 7. The points (3, five halves), (negative 1, 3), (negative 3, negative 4), and (2, negative 1) are all labeled.\" width=\"358\" height=\"365\" data-media-type=\"image\/png\" \/>\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146883[\/ohm_question]\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nHow do the signs affect the location of the points?\r\n\r\nPlot each point:\r\n\r\n1. [latex]\\left(-5,2\\right)[\/latex]\r\n2. [latex]\\left(-5,-2\\right)[\/latex]\r\n3. [latex]\\left(5,2\\right)[\/latex]\r\n4. [latex]\\left(5,-2\\right)[\/latex]\r\n[reveal-answer q=\"83169\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"83169\"]\r\n\r\nSolution\r\nAs we locate the [latex]x\\text{-coordinate}[\/latex] and the [latex]y\\text{-coordinate}[\/latex], we must be careful with the signs.\r\n\r\n<img class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224736\/CNX_BMath_Figure_11_01_028_img.png\" alt=\"The graph shows the x y-coordinate plane. The x and y-axis each run from -7 to 7. The points (5, 2), (negative 5, 2), (negative 5, negative 2), and (5, negative 2) are all labeled.\" width=\"253\" height=\"260\" data-media-type=\"image\/png\" \/>\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146885[\/ohm_question]\r\n\r\n<\/div>\r\nYou may have noticed some patterns as you graphed the points in the two previous examples. We can summarize sign patterns of the quadrants as follows. Also see the graph\u00a0below.\r\n<table id=\"eip-788\" summary=\"...\">\r\n<thead>\r\n<tr>\r\n<th style=\"width: 83px; text-align: left;\">Quadrant I<\/th>\r\n<th style=\"width: 87px;\">Quadrant II<\/th>\r\n<th style=\"width: 92px;\">Quadrant III<\/th>\r\n<th style=\"width: 94px;\">Quadrant IV<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 83px;\" data-align=\"center\">(<em data-effect=\"italics\">x<\/em>,<em data-effect=\"italics\">y<\/em>)<\/td>\r\n<td style=\"width: 87px;\" data-align=\"center\">(<em data-effect=\"italics\">x<\/em>,<em data-effect=\"italics\">y<\/em>)<\/td>\r\n<td style=\"width: 92px;\" data-align=\"center\">(<em data-effect=\"italics\">x<\/em>,<em data-effect=\"italics\">y<\/em>)<\/td>\r\n<td style=\"width: 94px;\" data-align=\"center\">(<em data-effect=\"italics\">x<\/em>,<em data-effect=\"italics\">y<\/em>)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 83px;\" data-align=\"center\">(+,+)<\/td>\r\n<td style=\"width: 87px;\" data-align=\"center\">(\u2212,+)<\/td>\r\n<td style=\"width: 92px;\" data-align=\"center\">(\u2212,\u2212)<\/td>\r\n<td style=\"width: 94px;\" data-align=\"center\">(+,\u2212)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224743\/CNX_BMath_Figure_11_01_013.png\" alt=\"The graph shows the x y-coordinate plane. The x and y-axis each run from -7 to 7. The top-right portion of the plane is labeled I with (+, +). The top-left portion of the place is labeled II with (-,+). The bottom-left portion of the table is labeled III with (-,-). The bottom-right portion of the table is labeled IV with (+,-).\" width=\"358\" height=\"365\" data-media-type=\"image\/png\" \/>\r\nWhat if one coordinate is zero? Where is the point [latex]\\left(0,4\\right)[\/latex] located? Where is the point [latex]\\left(-2,0\\right)[\/latex] located? The point [latex]\\left(0,4\\right)[\/latex] is on the [latex]y[\/latex]-axis and the point [latex]\\left(-2,0\\right)[\/latex] is on the [latex]x[\/latex]-axis.\r\n<div class=\"textbox shaded\">\r\n<h3>Points on the Axes<\/h3>\r\nPoints with a [latex]y\\text{-coordinate}[\/latex] equal to [latex]0[\/latex] are on the [latex]x[\/latex]-axis, and have coordinates [latex]\\left(a,0\\right)[\/latex].\r\n\r\nPoints with an [latex]x\\text{-coordinate}[\/latex] equal to [latex]0[\/latex] are on the [latex]y[\/latex]-axis, and have coordinates [latex]\\left(0,b\\right)[\/latex].\r\n\r\n<\/div>\r\nWhat is the ordered pair of the point where the axes cross? At that point both coordinates are zero, so its ordered pair is [latex]\\left(0,0\\right)[\/latex] . The point has a special name. It is called the <em data-effect=\"italics\">origin<\/em>.\r\n<div class=\"textbox shaded\">\r\n<h3>The Origin<\/h3>\r\nThe point [latex]\\left(0,0\\right)[\/latex] is called the <strong>origin<\/strong>. It is the point where the [latex]x[\/latex]-axis\u00a0and\u00a0[latex]y[\/latex]-axis\u00a0intersect.\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>ExAMPLE<\/h3>\r\nPlot each point on a coordinate grid:\r\n\r\n1. [latex]\\left(0,5\\right)[\/latex]\r\n2. [latex]\\left(4,0\\right)[\/latex]\r\n3. [latex]\\left(-3,0\\right)[\/latex]\r\n4. [latex]\\left(0,0\\right)[\/latex]\r\n5. [latex]\\left(0,-1\\right)[\/latex]\r\n[reveal-answer q=\"803167\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"803167\"]\r\n\r\nSolution\r\n<ol id=\"eip-id1164754129469\" class=\"circled\" data-number-style=\"arabic\">\r\n \t<li>Since [latex]x=0[\/latex], the point whose coordinates are [latex]\\left(0,5\\right)[\/latex] is on the [latex]y\\text{-axis}[\/latex].<\/li>\r\n \t<li>Since [latex]y=0[\/latex], the point whose coordinates are [latex]\\left(4,0\\right)[\/latex] is on the [latex]x\\text{-axis}[\/latex].<\/li>\r\n \t<li>Since [latex]y=0[\/latex], the point whose coordinates are [latex]\\left(-3,0\\right)[\/latex] is on the [latex]x\\text{-axis}[\/latex].<\/li>\r\n \t<li>Since [latex]x=0[\/latex] and [latex]y=0[\/latex], the point whose coordinates are [latex]\\left(0,0\\right)[\/latex] is the origin.<\/li>\r\n \t<li>Since [latex]x=0[\/latex], the point whose coordinates are [latex]\\left(0,-1\\right)[\/latex] is on the [latex]y\\text{-axis}[\/latex].\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224744\/CNX_BMath_Figure_11_01_031_img.png\" alt=\"The graph shows the x y-coordinate plane. The x and y-axis each run from -7 to 7. The points (0, 5), (4, 0), (0, 0), (negative 3, 0), and (0, negative 1) are all labeled.\" width=\"345\" height=\"352\" data-media-type=\"image\/png\" \/>[\/hidden-answer]<\/li>\r\n<\/ol>\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>TRY\u00a0IT<\/h3>\r\n[ohm_question]146886[\/ohm_question]\r\n\r\n<\/div>\r\nIn the following video, we show another example of how to plot several different points on the coordinate plane.\r\n\r\nhttps:\/\/youtu.be\/7JMXi_FxA2o\r\n<p data-type=\"title\">In data and graph analysis, being able to identify the coordinates of a point shown on a graph is just as important as being able to plot points. To identify the [latex]x[\/latex]-coordinate of a point on a graph, read the number on the [latex]x[\/latex]-axis\u00a0directly above or below the point. To identify the [latex]y[\/latex]-coordinate of a point, read the number on the [latex]y[\/latex]-axis\u00a0directly to the left or right of the point. Remember, to write the ordered pair using the correct order [latex]\\left(x,y\\right)[\/latex].<\/p>\r\n\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nName the ordered pair of each point shown:\r\n\r\n<img class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224748\/CNX_BMath_Figure_11_01_017.png\" alt=\"The graph shows the x y-coordinate plane. The x and y-axis each run from -7 to 7. The point (negative 3, 3) is labeled A. The point (negative 1, negative 3) is labeled B. The point (2, 4) is labaled C. The point (4, negative 4) is labeled D.\" width=\"258\" height=\"265\" data-media-type=\"image\/png\" \/>\r\n\r\nSolution\r\nPoint A is above [latex]-3[\/latex] on the [latex]x\\text{-axis}[\/latex], so the [latex]x\\text{-coordinate}[\/latex] of the point is [latex]-3[\/latex]. The point is to the left of [latex]3[\/latex] on the [latex]y\\text{-axis}[\/latex], so the [latex]y\\text{-coordinate}[\/latex] of the point is [latex]3[\/latex]. The coordinates of the point are [latex]\\left(-3,3\\right)[\/latex].\r\n\r\nPoint B is below [latex]-1[\/latex] on the [latex]x\\text{-axis}[\/latex], so the [latex]x\\text{-coordinate}[\/latex] of the point is [latex]-1[\/latex]. The point is to the left of [latex]-3[\/latex] on the [latex]y\\text{-axis}[\/latex], so the [latex]y\\text{-coordinate}[\/latex] of the point is [latex]-3[\/latex]. The coordinates of the point are [latex]\\left(-1,-3\\right)[\/latex].\r\n\r\nPoint C is above [latex]2[\/latex] on the [latex]x\\text{-axis}[\/latex], so the [latex]x\\text{-coordinate}[\/latex] of the point is [latex]2[\/latex]. The point is to the right of [latex]4[\/latex] on the [latex]y\\text{-axis}[\/latex], so the [latex]y\\text{-coordinate}[\/latex] of the point is [latex]4[\/latex]. The coordinates of the point are [latex]\\left(2,4\\right)[\/latex].\r\n\r\nPoint D is below [latex]4[\/latex] on the [latex]x-\\text{axis}[\/latex], so the [latex]x\\text{-coordinate}[\/latex] of the point is [latex]4[\/latex]. The point is to the right of [latex]-4[\/latex] on the [latex]y\\text{-axis}[\/latex], so the [latex]y\\text{-coordinate}[\/latex] of the point is [latex]-4[\/latex]. The coordinates of the point are [latex]\\left(4,-4\\right)[\/latex].\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146915[\/ohm_question]\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nName the ordered pair of each point shown:\r\n\r\n<img class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224752\/CNX_BMath_Figure_11_01_023.png\" alt=\"The graph shows the x y-coordinate plane. The x and y-axis each run from -7 to 7. The point (negative 4, 0) is labeled A. The point (0, negative 2) is labeled B. The point (3, 0) is labaled C. The point (0, 1) is labeled D.\" width=\"258\" height=\"265\" data-media-type=\"image\/png\" \/>\r\n[reveal-answer q=\"228616\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"228616\"]\r\n\r\nSolution\r\n<table id=\"eip-id2333867\" class=\"unnumbered unstyled\" style=\"width: 681px;\" summary=\".\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 283.9px;\">Point A is on the <em data-effect=\"italics\">x<\/em>-axis at [latex]x=-4[\/latex]<\/td>\r\n<td style=\"width: 373.1px;\">The coordinates of point A are [latex]\\left(-4,0\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 283.9px;\">Point B is on the <em data-effect=\"italics\">y<\/em>-axis at [latex]y=-2[\/latex]<\/td>\r\n<td style=\"width: 373.1px;\">The coordinates of point B are [latex]\\left(0,-2\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 283.9px;\">Point C is on the <em data-effect=\"italics\">x<\/em>-axis at [latex]x=3[\/latex]<\/td>\r\n<td style=\"width: 373.1px;\">The coordinates of point C are [latex]\\left(3,0\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 283.9px;\">Point D is on the <em data-effect=\"italics\">y-<\/em>axis at [latex]y=1[\/latex]<\/td>\r\n<td style=\"width: 373.1px;\">The coordinates of point D are [latex]\\left(0,1\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146919[\/ohm_question]\r\n\r\n<\/div>\r\nWatch the following video for another example of how to determine the ordered pair for points on the coordinate plane.\r\n\r\nhttps:\/\/youtu.be\/c9WVU34MY5Q","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning outcome<\/h3>\n<ul>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Graph points (ordered pairs) on a coordinate plane&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:13185,&quot;3&quot;:[null,0],&quot;10&quot;:2,&quot;11&quot;:4,&quot;12&quot;:0,&quot;15&quot;:&quot;Calibri&quot;,&quot;16&quot;:10}\">Graph points (ordered pairs) on a coordinate plane<\/span><\/li>\n<\/ul>\n<\/div>\n<p data-type=\"title\">Many maps, such as the Campus Map shown below, use a grid system to identify locations. Do you see the numbers [latex]1,2,3[\/latex], and [latex]4[\/latex] across the top and bottom of the map and the letters A, B, C, and D along the sides? Every location on the map can be identified by a number and a letter.<\/p>\n<p data-type=\"title\">For example, the Student Center is in section 2B. It is located in the grid section above the number [latex]2[\/latex] and next to the letter B. In which grid section is the Stadium? The Stadium is in section 4D.<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224708\/CNX_BMath_Figure_11_01_001.png\" alt=\"The figure shows a labeled grid representing the Campus Map. The columns are labeled 1 through 4 and the rows are labeled A through D. At position A-1 is the title Parking Garage. At position A-4 is a rectangle labeled Residence Halls. At position B-2 is a rectangle labeled Student Center. At position B-3 is a rectangle labeled Engineering Building. At position C-1 is a rectangle labeled Taylor Hall. At position C-2 is a rectangle labeled Library. At position C-4 is a rectangle labeled Tiger Field. At position D-4 is a rectangle labeled Stadium.\" data-media-type=\"image\/png\" \/><\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Use the map above.<\/p>\n<ol id=\"eip-id1164754238718\" class=\"circled\" data-number-style=\"arabic\">\n<li>Find the grid section of the Residence Halls.<\/li>\n<li>What is located in grid section 4C?<\/li>\n<\/ol>\n<p>Solution<\/p>\n<ol id=\"eip-id1164753925474\" class=\"circled\" data-number-style=\"arabic\">\n<li>Read the number below the Residence Halls, [latex]4[\/latex], and the letter to the side, A. So the Residence Halls are in grid section 4A.<\/li>\n<li>Find [latex]4[\/latex] across the bottom of the map and C along the side. Look below the [latex]4[\/latex] and next to the C. Tiger Field is in grid section 4C.<\/li>\n<\/ol>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146887\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146887&theme=oea&iframe_resize_id=ohm146887&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm146888\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146888&theme=oea&iframe_resize_id=ohm146888&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>Just as maps use a grid system to identify locations, a grid system is used in algebra to show a relationship between two variables in a rectangular coordinate system. To create a rectangular coordinate system, start with a horizontal number line. Show both positive and negative numbers as you did before, using a convenient scale unit. This horizontal number line is called the [latex]x[\/latex]-axis.<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224711\/CNX_BMath_Figure_11_01_026_img.png\" alt=\"The figure shows a number line with integer values labeled from -5 to 5.\" data-media-type=\"image\/png\" \/><br \/>\nNow, make a vertical number line passing through the [latex]x[\/latex]-axis at [latex]0[\/latex]. Put the positive numbers above [latex]0[\/latex] and the negative numbers below [latex]0[\/latex]. See the image below. This vertical line is called the[latex]y[\/latex]-axis.<\/p>\n<p>Vertical grid lines pass through the integers marked on the [latex]x[\/latex]-axis. Horizontal grid lines pass through the integers marked on the [latex]y[\/latex]-axis]. The resulting grid is the rectangular coordinate system.<\/p>\n<p>The rectangular coordinate system is also called the [latex]x\\text{-}y[\/latex] plane, the coordinate plane, or the Cartesian coordinate system (since it was developed by a mathematician named Ren\u00e9 Descartes.)<\/p>\n<div class=\"textbox shaded\">\n<h3>The rectangular coordinate system<\/h3>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224713\/CNX_BMath_Figure_11_01_002.png\" alt=\"The graph shows the x y-coordinate plane. The x and y-axis each run from -7 to 7. An arrow points to the horizontal axis with the label x-axis. An arrow points to the vertical axis with the label y-axis.\" width=\"367\" height=\"372\" data-media-type=\"image\/png\" \/><\/p>\n<\/div>\n<p>The [latex]x[\/latex]-axis] and the\u00a0[latex]y[\/latex]-axis form the rectangular coordinate system. These axes divide a plane into four areas, called quadrants. The quadrants are identified by Roman numerals, beginning on the upper right and proceeding counterclockwise. See the image below.<\/p>\n<div class=\"textbox shaded\">\n<h3>The four quadrants of the rectangular coordinate system<\/h3>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224716\/CNX_BMath_Figure_11_01_003.png\" alt=\"The graph shows the x y-coordinate plane. The x and y-axis each run from -7 to 7. The top-right portion of the plane is labeled I. The top-left portion of the place is labeled II. The bottom-left portion of the table is labeled III. The bottom-right portion of the table is labeled IV.\" width=\"345\" height=\"354\" data-media-type=\"image\/png\" \/><\/p>\n<\/div>\n<p>In the rectangular coordinate system, every point is represented by an ordered pair. The first number in the ordered pair is the <em data-effect=\"italics\">x<\/em>-coordinate of the point, and the second number is the <em data-effect=\"italics\">y<\/em>-coordinate of the point.<\/p>\n<div class=\"textbox shaded\">\n<h3>Ordered Pair<\/h3>\n<p>An ordered pair, [latex]\\left(x,y\\right)[\/latex] gives the coordinates of a point in a rectangular coordinate system.<\/p>\n<p>[latex]\\begin{array}{c}\\text{The first number is the }x\\text{-coordinate}.\\hfill \\\\ \\text{The second number is the }y\\text{-coordinate}.\\hfill \\end{array}[\/latex]<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224718\/CNX_BMath_Figure_11_01_027_img.png\" alt=\"The ordered pair x y is labeled with the first coordinate x labeled as x-coordinate and the second coordinate y labeled y-coordinate.\" width=\"226\" height=\"68\" data-media-type=\"image\/png\" \/><\/p>\n<\/div>\n<p>So how do the coordinates of a point help you locate a point on the [latex]x\\text{-}y[\/latex] plane?<\/p>\n<p>Let\u2019s try locating the point [latex]\\left(2,5\\right)[\/latex] . In this ordered pair, the [latex]x[\/latex] -coordinate is [latex]2[\/latex] and the [latex]y[\/latex] -coordinate is [latex]5[\/latex] .<\/p>\n<p>We start by locating the [latex]x[\/latex] value, [latex]2[\/latex], on the [latex]x\\text{-axis.}[\/latex] Then we lightly sketch a vertical line through [latex]x=2[\/latex], as shown in the image below.<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224719\/CNX_BMath_Figure_11_01_004.png\" alt=\"The graph shows the x y-coordinate plane. The x and y-axis each run from -6 to 6. There is a vertical dotted line passing through 2 on the x-axis.\" data-media-type=\"image\/png\" \/><br \/>\nNow we locate the [latex]y[\/latex] value, [latex]5[\/latex], on the [latex]y[\/latex] -axis and sketch a horizontal line through [latex]y=5[\/latex] . The point where these two lines meet is the point with coordinates [latex]\\left(2,5\\right)[\/latex]. We plot the point there, as shown in the image below.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224721\/CNX_BMath_Figure_11_01_005.png\" alt=\"The graph shows the x y-coordinate plane. The x and y-axis each run from -6 to 6. The point (2, 5) is labeled, and dashed vertical and horizontal lines run through this point.\" width=\"301\" height=\"308\" data-media-type=\"image\/png\" \/><\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Plot [latex]\\left(1,3\\right)[\/latex] and [latex]\\left(3,1\\right)[\/latex] in the same rectangular coordinate system.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q501893\">Show Answer<\/span><\/p>\n<div id=\"q501893\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<br \/>\nThe coordinate values are the same for both points, but the [latex]x[\/latex] and [latex]y[\/latex] values are reversed. Let\u2019s begin with point [latex]\\left(1,3\\right)[\/latex]. The [latex]x\\text{-coordinate}[\/latex] is [latex]1[\/latex] so find [latex]1[\/latex] on the [latex]x\\text{-axis}[\/latex] and sketch a vertical line through [latex]x=1[\/latex]. The [latex]y\\text{-coordinate}[\/latex] is [latex]3[\/latex] so we find [latex]3[\/latex] on the [latex]y\\text{-axis}[\/latex] and sketch a horizontal line through [latex]y=3[\/latex]. Where the two lines meet, we plot the point [latex]\\left(1,3\\right)[\/latex].<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224723\/CNX_BMath_Figure_11_01_006_img.png\" alt=\"The graph shows the x y-coordinate plane. The x and y-axis each run from -6 to 6. The point (1, 3) is labeled, and dashed vertical and horizontal lines run through this point.\" width=\"308\" height=\"316\" data-media-type=\"image\/png\" \/><br \/>\nTo plot the point [latex]\\left(3,1\\right)[\/latex], we start by locating [latex]3[\/latex] on the [latex]x\\text{-axis}[\/latex] and sketch a vertical line through [latex]x=3[\/latex]. Then we find [latex]1[\/latex] on the [latex]y\\text{-axis}[\/latex] and sketch a horizontal line through [latex]y=1[\/latex]. Where the two lines meet, we plot the point [latex]\\left(3,1\\right)[\/latex].<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224725\/CNX_BMath_Figure_11_01_007_img.png\" alt=\"The graph shows the x y-coordinate plane. The x and y-axis each run from -6 to 6. The point (3, 1) is labeled, and dashed vertical and horizontal lines run through this point. The point (1, 3) is also labeled.\" width=\"316\" height=\"323\" data-media-type=\"image\/png\" \/><br \/>\nNotice that the order of the coordinates does matter, so, [latex]\\left(1,3\\right)[\/latex] is not the same point as [latex]\\left(3,1\\right)[\/latex].<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146882\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146882&theme=oea&iframe_resize_id=ohm146882&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Exercises<\/h3>\n<p>Plot each point in the rectangular coordinate system and identify the quadrant in which the point is located:<\/p>\n<p>1. [latex]\\left(-1,3\\right)[\/latex]<br \/>\n2. [latex]\\left(-3,-4\\right)[\/latex]<br \/>\n3. [latex]\\left(2,-3\\right)[\/latex]<br \/>\n4. [latex]\\left(3,{\\Large\\frac{5}{2}}\\right)[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q933080\">Show Answer<\/span><\/p>\n<div id=\"q933080\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<br \/>\nThe first number of the coordinate pair is the [latex]x\\text{-coordinate}[\/latex], and the second number is the [latex]y\\text{-coordinate}[\/latex].<br \/>\n1. Since [latex]x=-1,y=3[\/latex], the point [latex]\\left(-1,3\\right)[\/latex] is in Quadrant II.<br \/>\n2. Since [latex]x=-3,y=-4[\/latex], the point [latex]\\left(-3,-4\\right)[\/latex] is in Quadrant III.<br \/>\n3. Since [latex]x=2,y=-1[\/latex], the point [latex]\\left(2,-1\\right)[\/latex] is in Quadrant lV.<br \/>\n4. Since [latex]x=3,y={\\Large\\frac{5}{2}}[\/latex], the point [latex]\\left(3,{\\Large\\frac{5}{2}}\\right)[\/latex] is in Quadrant I. It may be helpful to write [latex]{\\Large\\frac{5}{2}}[\/latex] as the mixed number, [latex]2{\\Large\\frac{1}{2}}[\/latex], or decimal, [latex]2.5[\/latex]. Then we know that the point is halfway between [latex]2[\/latex] and [latex]3[\/latex] on the [latex]y\\text{-axis}[\/latex].<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224731\/CNX_BMath_Figure_11_01_010.png\" alt=\"The graph shows the x y-coordinate plane. The x and y-axis each run from -7 to 7. The points (3, five halves), (negative 1, 3), (negative 3, negative 4), and (2, negative 1) are all labeled.\" width=\"358\" height=\"365\" data-media-type=\"image\/png\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146883\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146883&theme=oea&iframe_resize_id=ohm146883&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>How do the signs affect the location of the points?<\/p>\n<p>Plot each point:<\/p>\n<p>1. [latex]\\left(-5,2\\right)[\/latex]<br \/>\n2. [latex]\\left(-5,-2\\right)[\/latex]<br \/>\n3. [latex]\\left(5,2\\right)[\/latex]<br \/>\n4. [latex]\\left(5,-2\\right)[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q83169\">Show Answer<\/span><\/p>\n<div id=\"q83169\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<br \/>\nAs we locate the [latex]x\\text{-coordinate}[\/latex] and the [latex]y\\text{-coordinate}[\/latex], we must be careful with the signs.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224736\/CNX_BMath_Figure_11_01_028_img.png\" alt=\"The graph shows the x y-coordinate plane. The x and y-axis each run from -7 to 7. The points (5, 2), (negative 5, 2), (negative 5, negative 2), and (5, negative 2) are all labeled.\" width=\"253\" height=\"260\" data-media-type=\"image\/png\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146885\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146885&theme=oea&iframe_resize_id=ohm146885&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>You may have noticed some patterns as you graphed the points in the two previous examples. We can summarize sign patterns of the quadrants as follows. Also see the graph\u00a0below.<\/p>\n<table id=\"eip-788\" summary=\"...\">\n<thead>\n<tr>\n<th style=\"width: 83px; text-align: left;\">Quadrant I<\/th>\n<th style=\"width: 87px;\">Quadrant II<\/th>\n<th style=\"width: 92px;\">Quadrant III<\/th>\n<th style=\"width: 94px;\">Quadrant IV<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"width: 83px;\" data-align=\"center\">(<em data-effect=\"italics\">x<\/em>,<em data-effect=\"italics\">y<\/em>)<\/td>\n<td style=\"width: 87px;\" data-align=\"center\">(<em data-effect=\"italics\">x<\/em>,<em data-effect=\"italics\">y<\/em>)<\/td>\n<td style=\"width: 92px;\" data-align=\"center\">(<em data-effect=\"italics\">x<\/em>,<em data-effect=\"italics\">y<\/em>)<\/td>\n<td style=\"width: 94px;\" data-align=\"center\">(<em data-effect=\"italics\">x<\/em>,<em data-effect=\"italics\">y<\/em>)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 83px;\" data-align=\"center\">(+,+)<\/td>\n<td style=\"width: 87px;\" data-align=\"center\">(\u2212,+)<\/td>\n<td style=\"width: 92px;\" data-align=\"center\">(\u2212,\u2212)<\/td>\n<td style=\"width: 94px;\" data-align=\"center\">(+,\u2212)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224743\/CNX_BMath_Figure_11_01_013.png\" alt=\"The graph shows the x y-coordinate plane. The x and y-axis each run from -7 to 7. The top-right portion of the plane is labeled I with (+, +). The top-left portion of the place is labeled II with (-,+). The bottom-left portion of the table is labeled III with (-,-). The bottom-right portion of the table is labeled IV with (+,-).\" width=\"358\" height=\"365\" data-media-type=\"image\/png\" \/><br \/>\nWhat if one coordinate is zero? Where is the point [latex]\\left(0,4\\right)[\/latex] located? Where is the point [latex]\\left(-2,0\\right)[\/latex] located? The point [latex]\\left(0,4\\right)[\/latex] is on the [latex]y[\/latex]-axis and the point [latex]\\left(-2,0\\right)[\/latex] is on the [latex]x[\/latex]-axis.<\/p>\n<div class=\"textbox shaded\">\n<h3>Points on the Axes<\/h3>\n<p>Points with a [latex]y\\text{-coordinate}[\/latex] equal to [latex]0[\/latex] are on the [latex]x[\/latex]-axis, and have coordinates [latex]\\left(a,0\\right)[\/latex].<\/p>\n<p>Points with an [latex]x\\text{-coordinate}[\/latex] equal to [latex]0[\/latex] are on the [latex]y[\/latex]-axis, and have coordinates [latex]\\left(0,b\\right)[\/latex].<\/p>\n<\/div>\n<p>What is the ordered pair of the point where the axes cross? At that point both coordinates are zero, so its ordered pair is [latex]\\left(0,0\\right)[\/latex] . The point has a special name. It is called the <em data-effect=\"italics\">origin<\/em>.<\/p>\n<div class=\"textbox shaded\">\n<h3>The Origin<\/h3>\n<p>The point [latex]\\left(0,0\\right)[\/latex] is called the <strong>origin<\/strong>. It is the point where the [latex]x[\/latex]-axis\u00a0and\u00a0[latex]y[\/latex]-axis\u00a0intersect.<\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>ExAMPLE<\/h3>\n<p>Plot each point on a coordinate grid:<\/p>\n<p>1. [latex]\\left(0,5\\right)[\/latex]<br \/>\n2. [latex]\\left(4,0\\right)[\/latex]<br \/>\n3. [latex]\\left(-3,0\\right)[\/latex]<br \/>\n4. [latex]\\left(0,0\\right)[\/latex]<br \/>\n5. [latex]\\left(0,-1\\right)[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q803167\">Show Answer<\/span><\/p>\n<div id=\"q803167\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<ol id=\"eip-id1164754129469\" class=\"circled\" data-number-style=\"arabic\">\n<li>Since [latex]x=0[\/latex], the point whose coordinates are [latex]\\left(0,5\\right)[\/latex] is on the [latex]y\\text{-axis}[\/latex].<\/li>\n<li>Since [latex]y=0[\/latex], the point whose coordinates are [latex]\\left(4,0\\right)[\/latex] is on the [latex]x\\text{-axis}[\/latex].<\/li>\n<li>Since [latex]y=0[\/latex], the point whose coordinates are [latex]\\left(-3,0\\right)[\/latex] is on the [latex]x\\text{-axis}[\/latex].<\/li>\n<li>Since [latex]x=0[\/latex] and [latex]y=0[\/latex], the point whose coordinates are [latex]\\left(0,0\\right)[\/latex] is the origin.<\/li>\n<li>Since [latex]x=0[\/latex], the point whose coordinates are [latex]\\left(0,-1\\right)[\/latex] is on the [latex]y\\text{-axis}[\/latex].<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224744\/CNX_BMath_Figure_11_01_031_img.png\" alt=\"The graph shows the x y-coordinate plane. The x and y-axis each run from -7 to 7. The points (0, 5), (4, 0), (0, 0), (negative 3, 0), and (0, negative 1) are all labeled.\" width=\"345\" height=\"352\" data-media-type=\"image\/png\" \/><\/div>\n<\/div>\n<\/li>\n<\/ol>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>TRY\u00a0IT<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146886\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146886&theme=oea&iframe_resize_id=ohm146886&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>In the following video, we show another example of how to plot several different points on the coordinate plane.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Ex:  Plotting Points on the Coordinate Plane\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/7JMXi_FxA2o?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p data-type=\"title\">In data and graph analysis, being able to identify the coordinates of a point shown on a graph is just as important as being able to plot points. To identify the [latex]x[\/latex]-coordinate of a point on a graph, read the number on the [latex]x[\/latex]-axis\u00a0directly above or below the point. To identify the [latex]y[\/latex]-coordinate of a point, read the number on the [latex]y[\/latex]-axis\u00a0directly to the left or right of the point. Remember, to write the ordered pair using the correct order [latex]\\left(x,y\\right)[\/latex].<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Name the ordered pair of each point shown:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224748\/CNX_BMath_Figure_11_01_017.png\" alt=\"The graph shows the x y-coordinate plane. The x and y-axis each run from -7 to 7. The point (negative 3, 3) is labeled A. The point (negative 1, negative 3) is labeled B. The point (2, 4) is labaled C. The point (4, negative 4) is labeled D.\" width=\"258\" height=\"265\" data-media-type=\"image\/png\" \/><\/p>\n<p>Solution<br \/>\nPoint A is above [latex]-3[\/latex] on the [latex]x\\text{-axis}[\/latex], so the [latex]x\\text{-coordinate}[\/latex] of the point is [latex]-3[\/latex]. The point is to the left of [latex]3[\/latex] on the [latex]y\\text{-axis}[\/latex], so the [latex]y\\text{-coordinate}[\/latex] of the point is [latex]3[\/latex]. The coordinates of the point are [latex]\\left(-3,3\\right)[\/latex].<\/p>\n<p>Point B is below [latex]-1[\/latex] on the [latex]x\\text{-axis}[\/latex], so the [latex]x\\text{-coordinate}[\/latex] of the point is [latex]-1[\/latex]. The point is to the left of [latex]-3[\/latex] on the [latex]y\\text{-axis}[\/latex], so the [latex]y\\text{-coordinate}[\/latex] of the point is [latex]-3[\/latex]. The coordinates of the point are [latex]\\left(-1,-3\\right)[\/latex].<\/p>\n<p>Point C is above [latex]2[\/latex] on the [latex]x\\text{-axis}[\/latex], so the [latex]x\\text{-coordinate}[\/latex] of the point is [latex]2[\/latex]. The point is to the right of [latex]4[\/latex] on the [latex]y\\text{-axis}[\/latex], so the [latex]y\\text{-coordinate}[\/latex] of the point is [latex]4[\/latex]. The coordinates of the point are [latex]\\left(2,4\\right)[\/latex].<\/p>\n<p>Point D is below [latex]4[\/latex] on the [latex]x-\\text{axis}[\/latex], so the [latex]x\\text{-coordinate}[\/latex] of the point is [latex]4[\/latex]. The point is to the right of [latex]-4[\/latex] on the [latex]y\\text{-axis}[\/latex], so the [latex]y\\text{-coordinate}[\/latex] of the point is [latex]-4[\/latex]. The coordinates of the point are [latex]\\left(4,-4\\right)[\/latex].<\/p>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146915\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146915&theme=oea&iframe_resize_id=ohm146915&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Name the ordered pair of each point shown:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224752\/CNX_BMath_Figure_11_01_023.png\" alt=\"The graph shows the x y-coordinate plane. The x and y-axis each run from -7 to 7. The point (negative 4, 0) is labeled A. The point (0, negative 2) is labeled B. The point (3, 0) is labaled C. The point (0, 1) is labeled D.\" width=\"258\" height=\"265\" data-media-type=\"image\/png\" \/><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q228616\">Show Answer<\/span><\/p>\n<div id=\"q228616\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id2333867\" class=\"unnumbered unstyled\" style=\"width: 681px;\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td style=\"width: 283.9px;\">Point A is on the <em data-effect=\"italics\">x<\/em>-axis at [latex]x=-4[\/latex]<\/td>\n<td style=\"width: 373.1px;\">The coordinates of point A are [latex]\\left(-4,0\\right)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 283.9px;\">Point B is on the <em data-effect=\"italics\">y<\/em>-axis at [latex]y=-2[\/latex]<\/td>\n<td style=\"width: 373.1px;\">The coordinates of point B are [latex]\\left(0,-2\\right)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 283.9px;\">Point C is on the <em data-effect=\"italics\">x<\/em>-axis at [latex]x=3[\/latex]<\/td>\n<td style=\"width: 373.1px;\">The coordinates of point C are [latex]\\left(3,0\\right)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 283.9px;\">Point D is on the <em data-effect=\"italics\">y-<\/em>axis at [latex]y=1[\/latex]<\/td>\n<td style=\"width: 373.1px;\">The coordinates of point D are [latex]\\left(0,1\\right)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146919\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146919&theme=oea&iframe_resize_id=ohm146919&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>Watch the following video for another example of how to determine the ordered pair for points on the coordinate plane.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Determine the Ordered Pairs for Points Plotted on the Coordinate Plane\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/c9WVU34MY5Q?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-375\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Prealgebra. <strong>Provided by<\/strong>: OpenStax. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757<\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":17533,"menu_order":15,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Prealgebra\",\"author\":\"\",\"organization\":\"OpenStax\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757\"}]","CANDELA_OUTCOMES_GUID":"b6c59980-0701-4248-a23a-f0a739f6282e, 22696078-bb41-48a0-b825-c22490e6bd30","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-375","chapter","type-chapter","status-publish","hentry"],"part":26,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/pressbooks\/v2\/chapters\/375","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/wp\/v2\/users\/17533"}],"version-history":[{"count":12,"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/pressbooks\/v2\/chapters\/375\/revisions"}],"predecessor-version":[{"id":4004,"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/pressbooks\/v2\/chapters\/375\/revisions\/4004"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/pressbooks\/v2\/parts\/26"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/pressbooks\/v2\/chapters\/375\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/wp\/v2\/media?parent=375"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/pressbooks\/v2\/chapter-type?post=375"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/wp\/v2\/contributor?post=375"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/wp\/v2\/license?post=375"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}