{"id":2362,"date":"2021-10-12T13:22:49","date_gmt":"2021-10-12T13:22:49","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/?post_type=chapter&#038;p=2362"},"modified":"2022-04-24T02:43:35","modified_gmt":"2022-04-24T02:43:35","slug":"plotting-points-on-the-coordinate-plane","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/chapter\/plotting-points-on-the-coordinate-plane\/","title":{"raw":"Plotting Points on the Coordinate Plane","rendered":"Plotting Points on the Coordinate Plane"},"content":{"raw":"<div class=\"bcc-box bcc-highlight\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Plot points on a rectangular coordinate system<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h2>Rectangular Coordinate System<\/h2>\r\nThe coordinate plane has similar elements to the grid shown above. Look at the Rectangular Coordinate System shown in the box below. It consists of a horizontal <b>axis<\/b> and a vertical axis: number lines that intersect at right angles. (They are perpendicular to each other).\r\n\r\nThe horizontal axis in the coordinate plane is called the [latex]x-axis[\/latex]. The vertical axis is called the [latex]y-axis[\/latex]. The point at which the two axes intersect is called the <b>origin<\/b>. The origin is at [latex]0[\/latex] on the [latex]x-axis[\/latex] and [latex]0[\/latex] on the [latex]y-axis[\/latex].\r\n\r\nThe intersecting <i>x-<\/i> and <i>y-<\/i>axes of the coordinate plane divide it\u00a0into four sections. These four sections are called <b>quadrants<\/b>. Quadrants are named using the Roman numerals I, II, III, and IV beginning with the top right quadrant and moving counterclockwise.\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-archive-read-only\/wp-content\/uploads\/sites\/1468\/2016\/02\/04064227\/image002.jpg\" alt=\"A graph with an x-axis running horizontally and a y-axis running vertically. The location where these axes cross is labeled the origin, and is the point zero, zero. The axes also divide the graph into four equal quadrants. The top right area is quadrant one. The top left area is quadrant two. The bottom left area is quadrant three. The bottom right area is quadrant four.\" width=\"417\" height=\"378\" \/>\r\n\r\n<\/div>\r\nLocations on the coordinate plane are described as <b>ordered pairs<\/b>. An ordered pair tells you the location of a point by relating the point\u2019s location along the <i>x-<\/i>axis (the first value of the ordered pair) and along the [latex]y-axis[\/latex] (the second value of the ordered pair).\r\n\r\nIn an ordered pair, such as [latex](x, y)[\/latex], the first value is called the <b>x-coordinate<\/b> and the second value is the <b>y-coordinate<\/b>. Note that the <i>x-<\/i>coordinate is listed before the <i>y-<\/i>coordinate. Since the origin has an <i>x-<\/i>coordinate of [latex]0[\/latex] and a <i>y-<\/i>coordinate of [latex]0[\/latex], its ordered pair is written [latex](0, 0)[\/latex].\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 \u201cx-coordinate\u201d and the second coordinate y labeled as \u201cy-coordinate\u201d\" width=\"226\" height=\"68\" \/>\r\n\r\n<\/div>\r\n<h2 id=\"Plotting Points in the Coordinate Plane\" class=\"no-indent\" style=\"text-align: left;\">Plotting Points in the Coordinate Plane<\/h2>\r\nNow that you know the components of a rectangular system, let's learn how to plot ordered pairs, that is locate a point on the coordinate system given an ordered pair. Just remember, the process starts at the origin\u2014the beginning!\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.\" \/>\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. An arrow starts at the origin and extends right to the number 2 on the x-axis. An arrow starts at the end of the first arrow at 2 on the x-axis and goes vertically 5 units to a point labeled \u201c2, 5\u201d in parentheses.\" width=\"301\" height=\"308\" \/>\r\n\r\n<span style=\"color: #ff0000;\">Reminder:<\/span>\u00a0Any ordered pair, such as (2,5), represents one single point on the graph.\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 Solution[\/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. A horizontal dotted line passes through 3 on the y axis. A vertical dotted line passes through 1 on the x axis. The dotted lines intersect at a point labeled \u201cordered pair 1, 3\u201d.\" width=\"308\" height=\"316\" \/>\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. A horizontal dotted line passes through 1 on the y-axis. A vertical dotted line passes through 3 on the x axis. The dotted lines intersect at a point labeled \u201cordered pair 3, 1\u201d.\" width=\"316\" height=\"323\" \/>\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\nNow, let's take another look at how to plot the ordered pair (1,3). The method shown below is slightly different from the method shown above, but it yields the same result.\r\n<div class=\"bcc-box bcc-info\">\r\n<h3>Example<\/h3>\r\nPlot the point [latex](1, 3)[\/latex].\r\n\r\n[reveal-answer q=\"28562\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"28562\"]\r\n\r\nThe <i>x-<\/i>coordinate is [latex]1[\/latex] because it comes first in the ordered pair. Start at the origin and move a distance of [latex]1[\/latex] unit in a positive direction (to the right) from the origin along the <i>x-<\/i>axis.\r\n\r\nThe <i>y-<\/i>coordinate is [latex]3[\/latex] because it comes second in the ordered pair. From here move directly [latex]3[\/latex] units in a positive direction (up). If you look over to the <i>y-<\/i>axis, you should be lined up with [latex]3[\/latex] on that axis.\r\n<h4>Answer<\/h4>\r\nDraw a point at this location and label the point [latex](1, 3)[\/latex].<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1468\/2016\/02\/04064232\/image005.jpg\" alt=\"Graph. A blue arrow goes from the origin (the point 0,0) to one unit to the right. A red arrow goes from the blue arrow to 3 units above the x-axis. That point is (1,3).\" width=\"417\" height=\"378\" \/>[\/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\nIn the previous examples, both the <i>x-<\/i> and <i>y-<\/i>coordinates were positive. When one (or both) of the coordinates of an ordered pair is negative, you will need to move in the negative direction along one or both axes. Consider the example below in which both coordinates are negative.\r\n<div class=\"bcc-box bcc-info\">\r\n<h3>Example<\/h3>\r\nPlot the point [latex](\u22124,\u22122)[\/latex].\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1468\/2016\/02\/04064233\/image006.jpg\" alt=\"Graph with blue arrow pointing from origin to four units to the left. A red arrow points down 2 spaces to the point negative 4, negative 2.\" width=\"417\" height=\"378\" \/>\r\n\r\nThe <i>x-<\/i>coordinate is [latex]\u22124[\/latex] because it comes first in the ordered pair. Start at the origin and move [latex]4[\/latex] units in a negative direction (left) along the <i>x-<\/i>axis.\r\n\r\nThe <i>y-<\/i>coordinate is [latex]\u22122[\/latex] because it comes second in the ordered pair. Now move [latex]2[\/latex] units in a negative direction (down). If you look over to the <i>y-<\/i>axis, you should be lined up with [latex]\u22122[\/latex] on that axis.\r\n\r\nNow draw a point at that location and label it.\r\n\r\n<\/div>\r\nThe steps for plotting a point are summarized below.\r\n<div class=\"textbox shaded\">\r\n<h3>Steps for Plotting an Ordered Pair (<i>x<\/i>, <i>y<\/i>) in the Coordinate Plane<\/h3>\r\n<ul>\r\n \t<li>Determine the <i>x-<\/i>coordinate. Beginning at the origin, move horizontally, the direction of the <i>x<\/i>-axis, the distance given by the <i>x-<\/i>coordinate. If the <i>x-<\/i>coordinate is positive, move to the right; if the <i>x-<\/i>coordinate is negative, move to the left.<\/li>\r\n \t<li>Determine the <i>y-<\/i>coordinate. Beginning at the <i>x-<\/i>coordinate, move vertically, the direction of the <i>y<\/i>-axis, the distance given by the <i>y-<\/i>coordinate. If the <i>y-<\/i>coordinate is positive, move up; if the <i>y-<\/i>coordinate is negative, move down.<\/li>\r\n \t<li>Draw a point at the ending location. Label the point with the ordered pair.<\/li>\r\n \t<li>An ordered pair is represented by a <strong>single<\/strong> point on the graph.<\/li>\r\n<\/ul>\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 Solution[\/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 point \u201cordered pair 5, 2\u201d is labeled \u201cordered pair 5, 2\u201d. The point \u201cordered pair -5, 2\u201d is labeled \u201cordered pair -5, 2\u201d. The point \u201cordered pair -5, -2\u201d is labeled \u201cordered pair -5, -2\u201d. The point \u201cordered pair 5, -2\u201d is labeled \u201cordered pair 5, -2\u201d.\" width=\"253\" height=\"260\" \/>\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\n<p id=\"video2\" class=\"no-indent\" style=\"text-align: left;\">Watch the video below for more examples of how to plot ordered pairs.<\/p>\r\nhttps:\/\/youtu.be\/p_MESleS3mw\r\n<h2 id=\"Introduction\" class=\"no-indent\" style=\"text-align: left;\"><\/h2>","rendered":"<div class=\"bcc-box bcc-highlight\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Plot points on a rectangular coordinate system<\/li>\n<\/ul>\n<\/div>\n<h2>Rectangular Coordinate System<\/h2>\n<p>The coordinate plane has similar elements to the grid shown above. Look at the Rectangular Coordinate System shown in the box below. It consists of a horizontal <b>axis<\/b> and a vertical axis: number lines that intersect at right angles. (They are perpendicular to each other).<\/p>\n<p>The horizontal axis in the coordinate plane is called the [latex]x-axis[\/latex]. The vertical axis is called the [latex]y-axis[\/latex]. The point at which the two axes intersect is called the <b>origin<\/b>. The origin is at [latex]0[\/latex] on the [latex]x-axis[\/latex] and [latex]0[\/latex] on the [latex]y-axis[\/latex].<\/p>\n<p>The intersecting <i>x-<\/i> and <i>y-<\/i>axes of the coordinate plane divide it\u00a0into four sections. These four sections are called <b>quadrants<\/b>. Quadrants are named using the Roman numerals I, II, III, and IV beginning with the top right quadrant and moving counterclockwise.<\/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-archive-read-only\/wp-content\/uploads\/sites\/1468\/2016\/02\/04064227\/image002.jpg\" alt=\"A graph with an x-axis running horizontally and a y-axis running vertically. The location where these axes cross is labeled the origin, and is the point zero, zero. The axes also divide the graph into four equal quadrants. The top right area is quadrant one. The top left area is quadrant two. The bottom left area is quadrant three. The bottom right area is quadrant four.\" width=\"417\" height=\"378\" \/><\/p>\n<\/div>\n<p>Locations on the coordinate plane are described as <b>ordered pairs<\/b>. An ordered pair tells you the location of a point by relating the point\u2019s location along the <i>x-<\/i>axis (the first value of the ordered pair) and along the [latex]y-axis[\/latex] (the second value of the ordered pair).<\/p>\n<p>In an ordered pair, such as [latex](x, y)[\/latex], the first value is called the <b>x-coordinate<\/b> and the second value is the <b>y-coordinate<\/b>. Note that the <i>x-<\/i>coordinate is listed before the <i>y-<\/i>coordinate. Since the origin has an <i>x-<\/i>coordinate of [latex]0[\/latex] and a <i>y-<\/i>coordinate of [latex]0[\/latex], its ordered pair is written [latex](0, 0)[\/latex].<\/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 \u201cx-coordinate\u201d and the second coordinate y labeled as \u201cy-coordinate\u201d\" width=\"226\" height=\"68\" \/><\/p>\n<\/div>\n<h2 id=\"Plotting Points in the Coordinate Plane\" class=\"no-indent\" style=\"text-align: left;\">Plotting Points in the Coordinate Plane<\/h2>\n<p>Now that you know the components of a rectangular system, let&#8217;s learn how to plot ordered pairs, that is locate a point on the coordinate system given an ordered pair. Just remember, the process starts at the origin\u2014the beginning!<\/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.\" \/><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. An arrow starts at the origin and extends right to the number 2 on the x-axis. An arrow starts at the end of the first arrow at 2 on the x-axis and goes vertically 5 units to a point labeled \u201c2, 5\u201d in parentheses.\" width=\"301\" height=\"308\" \/><\/p>\n<p><span style=\"color: #ff0000;\">Reminder:<\/span>\u00a0Any ordered pair, such as (2,5), represents one single point on the graph.<\/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 Solution<\/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. A horizontal dotted line passes through 3 on the y axis. A vertical dotted line passes through 1 on the x axis. The dotted lines intersect at a point labeled \u201cordered pair 1, 3\u201d.\" width=\"308\" height=\"316\" \/><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. A horizontal dotted line passes through 1 on the y-axis. A vertical dotted line passes through 3 on the x axis. The dotted lines intersect at a point labeled \u201cordered pair 3, 1\u201d.\" width=\"316\" height=\"323\" \/><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<p>Now, let&#8217;s take another look at how to plot the ordered pair (1,3). The method shown below is slightly different from the method shown above, but it yields the same result.<\/p>\n<div class=\"bcc-box bcc-info\">\n<h3>Example<\/h3>\n<p>Plot the point [latex](1, 3)[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q28562\">Show Solution<\/span><\/p>\n<div id=\"q28562\" class=\"hidden-answer\" style=\"display: none\">\n<p>The <i>x-<\/i>coordinate is [latex]1[\/latex] because it comes first in the ordered pair. Start at the origin and move a distance of [latex]1[\/latex] unit in a positive direction (to the right) from the origin along the <i>x-<\/i>axis.<\/p>\n<p>The <i>y-<\/i>coordinate is [latex]3[\/latex] because it comes second in the ordered pair. From here move directly [latex]3[\/latex] units in a positive direction (up). If you look over to the <i>y-<\/i>axis, you should be lined up with [latex]3[\/latex] on that axis.<\/p>\n<h4>Answer<\/h4>\n<p>Draw a point at this location and label the point [latex](1, 3)[\/latex].<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1468\/2016\/02\/04064232\/image005.jpg\" alt=\"Graph. A blue arrow goes from the origin (the point 0,0) to one unit to the right. A red arrow goes from the blue arrow to 3 units above the x-axis. That point is (1,3).\" width=\"417\" height=\"378\" \/><\/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<p>In the previous examples, both the <i>x-<\/i> and <i>y-<\/i>coordinates were positive. When one (or both) of the coordinates of an ordered pair is negative, you will need to move in the negative direction along one or both axes. Consider the example below in which both coordinates are negative.<\/p>\n<div class=\"bcc-box bcc-info\">\n<h3>Example<\/h3>\n<p>Plot the point [latex](\u22124,\u22122)[\/latex].<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1468\/2016\/02\/04064233\/image006.jpg\" alt=\"Graph with blue arrow pointing from origin to four units to the left. A red arrow points down 2 spaces to the point negative 4, negative 2.\" width=\"417\" height=\"378\" \/><\/p>\n<p>The <i>x-<\/i>coordinate is [latex]\u22124[\/latex] because it comes first in the ordered pair. Start at the origin and move [latex]4[\/latex] units in a negative direction (left) along the <i>x-<\/i>axis.<\/p>\n<p>The <i>y-<\/i>coordinate is [latex]\u22122[\/latex] because it comes second in the ordered pair. Now move [latex]2[\/latex] units in a negative direction (down). If you look over to the <i>y-<\/i>axis, you should be lined up with [latex]\u22122[\/latex] on that axis.<\/p>\n<p>Now draw a point at that location and label it.<\/p>\n<\/div>\n<p>The steps for plotting a point are summarized below.<\/p>\n<div class=\"textbox shaded\">\n<h3>Steps for Plotting an Ordered Pair (<i>x<\/i>, <i>y<\/i>) in the Coordinate Plane<\/h3>\n<ul>\n<li>Determine the <i>x-<\/i>coordinate. Beginning at the origin, move horizontally, the direction of the <i>x<\/i>-axis, the distance given by the <i>x-<\/i>coordinate. If the <i>x-<\/i>coordinate is positive, move to the right; if the <i>x-<\/i>coordinate is negative, move to the left.<\/li>\n<li>Determine the <i>y-<\/i>coordinate. Beginning at the <i>x-<\/i>coordinate, move vertically, the direction of the <i>y<\/i>-axis, the distance given by the <i>y-<\/i>coordinate. If the <i>y-<\/i>coordinate is positive, move up; if the <i>y-<\/i>coordinate is negative, move down.<\/li>\n<li>Draw a point at the ending location. Label the point with the ordered pair.<\/li>\n<li>An ordered pair is represented by a <strong>single<\/strong> point on the graph.<\/li>\n<\/ul>\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 Solution<\/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 point \u201cordered pair 5, 2\u201d is labeled \u201cordered pair 5, 2\u201d. The point \u201cordered pair -5, 2\u201d is labeled \u201cordered pair -5, 2\u201d. The point \u201cordered pair -5, -2\u201d is labeled \u201cordered pair -5, -2\u201d. The point \u201cordered pair 5, -2\u201d is labeled \u201cordered pair 5, -2\u201d.\" width=\"253\" height=\"260\" \/><\/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 id=\"video2\" class=\"no-indent\" style=\"text-align: left;\">Watch the video below for more examples of how to plot ordered pairs.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Plot Points Given as Ordered Pairs on the Coordinate Plane\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/p_MESleS3mw?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<h2 id=\"Introduction\" class=\"no-indent\" style=\"text-align: left;\"><\/h2>\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-2362\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">All rights reserved content<\/div><ul class=\"citation-list\"><li>Plot Points Given as Ordered Pairs on the Coordinate Plane. <strong>Authored by<\/strong>: mathispower4u. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/p_MESleS3mw\">https:\/\/youtu.be\/p_MESleS3mw<\/a>. <strong>License<\/strong>: <em>All Rights Reserved<\/em>. <strong>License Terms<\/strong>: Standard YouTube License<\/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":169134,"menu_order":3,"template":"","meta":{"_candela_citation":"[{\"type\":\"copyrighted_video\",\"description\":\"Plot Points Given as Ordered Pairs on the Coordinate Plane\",\"author\":\"mathispower4u\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/p_MESleS3mw\",\"project\":\"\",\"license\":\"arr\",\"license_terms\":\"Standard YouTube License\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-2362","chapter","type-chapter","status-publish","hentry"],"part":303,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/2362","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/users\/169134"}],"version-history":[{"count":7,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/2362\/revisions"}],"predecessor-version":[{"id":4018,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/2362\/revisions\/4018"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/parts\/303"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/2362\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/media?parent=2362"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapter-type?post=2362"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/contributor?post=2362"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/license?post=2362"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}