{"id":10672,"date":"2017-06-05T14:58:01","date_gmt":"2017-06-05T14:58:01","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/prealgebra\/?post_type=chapter&#038;p=10672"},"modified":"2020-10-22T09:15:12","modified_gmt":"2020-10-22T09:15:12","slug":"identifying-points-on-the-rectangular-coordinate-system","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/chapter\/identifying-points-on-the-rectangular-coordinate-system\/","title":{"raw":"9.1.b - Identifying Points on a Rectangular Coordinate System","rendered":"9.1.b &#8211; Identifying Points on a Rectangular Coordinate System"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Identify points on a graph<\/li>\r\n<\/ul>\r\n<\/div>\r\nIn algebra, 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 <em>x<\/em>-coordinate of a point on a graph, read the number on the <em>x<\/em>-axis directly above or below the point. To identify the <em>y<\/em>-coordinate of a point, read the number on the <em>y<\/em>-axis directly to the left or right of the point. Remember, to write the ordered pair using the correct order [latex]\\left(x,y\\right)[\/latex].\r\n\r\nConsider the point below.\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\/04064228\/image003-1.jpg\" alt=\"Grid with x-axis and y-axis. A blue dotted line extends from the origin, which is the point (0,0) along the horizontal x-axis to 4. A red dotted line goes up vertically from 4 on the x-axis to 3 on the y-axis. That point is labeled (4, 3).\" width=\"417\" height=\"378\" \/>\r\n\r\nTo identify the location of this point, start at the origin [latex](0, 0)[\/latex] and move right along the <i>x-<\/i>axis until you are under the point. Look at the label on the <i>x-<\/i>axis. The [latex]4[\/latex] indicates that, from the origin, you have traveled four units to the right along the <i>x<\/i>-axis. This is the <i>x-<\/i>coordinate, the first number in the ordered pair.\r\n\r\nFrom [latex]4[\/latex] on the <i>x-<\/i>axis move up to the point and notice the number with which it aligns on the <i>y-<\/i>axis. The [latex]3[\/latex] indicates that, after leaving the <i>x<\/i>-axis, you traveled [latex]3[\/latex] units up in the vertical direction, the direction of the <i>y<\/i>-axis. This number is the <i>y-<\/i>coordinate, the second number in the ordered pair. With an <i>x-<\/i>coordinate of [latex]4[\/latex] and a <i>y-<\/i>coordinate of [latex]3[\/latex], you have the ordered pair [latex](4, 3)[\/latex].\r\n\r\nLet\u2019s look at another example.\r\n<div class=\"bcc-box bcc-info\">\r\n<h3>Example<\/h3>\r\nDescribe the point shown as an ordered pair.\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\/04064229\/image004-1.jpg\" alt=\"A point that is 2 spaces above the x-axis and 5 spaces to the right of the y-axis.\" width=\"417\" height=\"378\" \/>\r\n\r\n[reveal-answer q=\"668288\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"668288\"]\r\n\r\nBegin at the origin and move along the <i>x-<\/i>axis. This is the <i>x-<\/i>coordinate and is written first in the ordered pair.\r\n<p style=\"text-align: center\">[latex](5,<i>y<\/i>)[\/latex]<\/p>\r\nMove from 5 up to the ordered pair and read the number on the <i>y-<\/i>axis. This is the <i>y-<\/i>coordinate and is written second in the ordered pair.\r\n<p style=\"text-align: center\">[latex](5,2)[\/latex]<\/p>\r\n\r\n<h4>Answer<\/h4>\r\nThe point shown as an ordered pair is [latex](5,2)[\/latex].[\/hidden-answer]\r\n\r\n<\/div>\r\n<h2>Describe the point shown as an ordered pair<\/h2>\r\nhttps:\/\/youtu.be\/c9WVU34MY5Q\r\n\r\n&nbsp;\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 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 \" \/>\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&nbsp;\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&nbsp;\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 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 \" \/>\r\n[reveal-answer q=\"228616\"]Show Solution[\/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=\".\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 283.9px\">Point A is on the <em>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>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>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>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&nbsp;\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 Outcomes<\/h3>\n<ul>\n<li>Identify points on a graph<\/li>\n<\/ul>\n<\/div>\n<p>In algebra, 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 <em>x<\/em>-coordinate of a point on a graph, read the number on the <em>x<\/em>-axis directly above or below the point. To identify the <em>y<\/em>-coordinate of a point, read the number on the <em>y<\/em>-axis directly 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<p>Consider the point below.<\/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\/04064228\/image003-1.jpg\" alt=\"Grid with x-axis and y-axis. A blue dotted line extends from the origin, which is the point (0,0) along the horizontal x-axis to 4. A red dotted line goes up vertically from 4 on the x-axis to 3 on the y-axis. That point is labeled (4, 3).\" width=\"417\" height=\"378\" \/><\/p>\n<p>To identify the location of this point, start at the origin [latex](0, 0)[\/latex] and move right along the <i>x-<\/i>axis until you are under the point. Look at the label on the <i>x-<\/i>axis. The [latex]4[\/latex] indicates that, from the origin, you have traveled four units to the right along the <i>x<\/i>-axis. This is the <i>x-<\/i>coordinate, the first number in the ordered pair.<\/p>\n<p>From [latex]4[\/latex] on the <i>x-<\/i>axis move up to the point and notice the number with which it aligns on the <i>y-<\/i>axis. The [latex]3[\/latex] indicates that, after leaving the <i>x<\/i>-axis, you traveled [latex]3[\/latex] units up in the vertical direction, the direction of the <i>y<\/i>-axis. This number is the <i>y-<\/i>coordinate, the second number in the ordered pair. With an <i>x-<\/i>coordinate of [latex]4[\/latex] and a <i>y-<\/i>coordinate of [latex]3[\/latex], you have the ordered pair [latex](4, 3)[\/latex].<\/p>\n<p>Let\u2019s look at another example.<\/p>\n<div class=\"bcc-box bcc-info\">\n<h3>Example<\/h3>\n<p>Describe the point shown as an ordered pair.<\/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\/04064229\/image004-1.jpg\" alt=\"A point that is 2 spaces above the x-axis and 5 spaces to the right of the y-axis.\" width=\"417\" height=\"378\" \/><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q668288\">Show Solution<\/span><\/p>\n<div id=\"q668288\" class=\"hidden-answer\" style=\"display: none\">\n<p>Begin at the origin and move along the <i>x-<\/i>axis. This is the <i>x-<\/i>coordinate and is written first in the ordered pair.<\/p>\n<p style=\"text-align: center\">[latex](5,<i>y<\/i>)[\/latex]<\/p>\n<p>Move from 5 up to the ordered pair and read the number on the <i>y-<\/i>axis. This is the <i>y-<\/i>coordinate and is written second in the ordered pair.<\/p>\n<p style=\"text-align: center\">[latex](5,2)[\/latex]<\/p>\n<h4>Answer<\/h4>\n<p>The point shown as an ordered pair is [latex](5,2)[\/latex].<\/p><\/div>\n<\/div>\n<\/div>\n<h2>Describe the point shown as an ordered pair<\/h2>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" 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<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Name the ordered pair of each point shown:<\/p>\n<p><img decoding=\"async\" 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\" \/><\/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<p>&nbsp;<\/p>\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<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Name the ordered pair of each point shown:<\/p>\n<p><img decoding=\"async\" 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\" \/><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q228616\">Show Solution<\/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=\".\">\n<tbody>\n<tr>\n<td style=\"width: 283.9px\">Point A is on the <em>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>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>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>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<p>&nbsp;<\/p>\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-10672\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li>Question ID 146919, 146915, 146888, 146887, 146886, 146885, 146883. <strong>Authored by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Determine the Ordered Pairs for Points Plotted on the Coordinate Plane. <strong>Authored by<\/strong>: James Sousa (mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/c9WVU34MY5Q\">https:\/\/youtu.be\/c9WVU34MY5Q<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Specific attribution<\/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":4,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"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\"},{\"type\":\"original\",\"description\":\"Question ID 146919, 146915, 146888, 146887, 146886, 146885, 146883\",\"author\":\"Lumen Learning\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Determine the Ordered Pairs for Points Plotted on the Coordinate Plane\",\"author\":\"James Sousa (mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/c9WVU34MY5Q\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"04dcacf26ac2496eb29551e7708e024a, 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