{"id":4605,"date":"2017-06-07T18:52:48","date_gmt":"2017-06-07T18:52:48","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/aacc-collegealgebrafoundations\/chapter\/read-quadrants-on-the-coordinate-plane\/"},"modified":"2017-08-16T02:48:56","modified_gmt":"2017-08-16T02:48:56","slug":"read-quadrants-on-the-coordinate-plane","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/aacc-collegealgebrafoundations\/chapter\/read-quadrants-on-the-coordinate-plane\/","title":{"raw":"Quadrants on the Coordinate Plane","rendered":"Quadrants on the Coordinate Plane"},"content":{"raw":"<div class=\"bcc-box bcc-highlight\">\r\n<h3>Learning Objectives<\/h3>\r\n<ul>\r\n \t<li>Identify Quadrants on the Coordinate Plane\r\n<ul>\r\n \t<li>Identify the four quadrants of a coordinate plane<\/li>\r\n \t<li>Given an ordered pair, determine its quadrant<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h2 class=\"no-indent\" style=\"text-align: left\"><span style=\"color: #4a92c2\">Identify quadrants and use them to plot points<\/span><\/h2>\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 counter clockwise.\r\n\r\nOrdered pairs within any particular quadrant share certain characteristics. Look at each quadrant in the graph below. What do you notice about the signs of the <i>x-<\/i> and <i>y-<\/i>coordinates of the points within each quadrant?\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2011\/2017\/06\/07185241\/image008-1.jpg\" alt=\"A graph with many plotted points in different quadrants. Quadrant 1 has the point (1,3); the point (2,2); and the point (4,1). Quadrant 2 has the point negative 1, one; the point negative 2, 5; and the point negative 4, one. Quadrant 3 has the point negative 2, negative 3; the point negative 3, negative 3; and the point negative 1, negative 5. Quadrant 4 has the point 2, negative 1; the point 1, negative 3; and the point 4, negative 4.\" width=\"417\" height=\"378\" \/>\r\n\r\nWithin each quadrant, the signs of the <i>x-<\/i>coordinates and <i>y-<\/i>coordinates of each ordered pair are the same. They also follow a pattern, which is outlined in the table below.\r\n<table>\r\n<thead>\r\n<tr>\r\n<th>Quadrant<\/th>\r\n<th>General Form of Point in this Quadrant<\/th>\r\n<th>Example<\/th>\r\n<th>Description<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td>I<\/td>\r\n<td>[latex](+,+)[\/latex]<\/td>\r\n<td>[latex](5,4)[\/latex]<\/td>\r\n<td>Starting from the origin, go along the <i>x-<\/i>axis in a positive direction (right) and along the <i>y-<\/i>axis in a positive direction (up).<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>II<\/td>\r\n<td>[latex](\u2212,+)[\/latex]<\/td>\r\n<td>[latex](\u22125,4)[\/latex]<\/td>\r\n<td>Starting from the origin, go along the <i>x-<\/i>axis in a negative direction (left) and along the <i>y-<\/i>axis in a positive direction (up).<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>III<\/td>\r\n<td>[latex](\u2212,\u2212)[\/latex]<\/td>\r\n<td>[latex](\u22125,\u22124)[\/latex]<\/td>\r\n<td>Starting from the origin, go along the <i>x-<\/i>axis in a negative direction (left) and along the <i>y-<\/i>axis in a negative direction (down).<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>IV<\/td>\r\n<td>[latex](+,\u2212)[\/latex]<\/td>\r\n<td>[latex](5,\u22124)[\/latex]<\/td>\r\n<td>Starting from the origin, go along the <i>x-<\/i>axis in a positive direction (right) and along the <i>y-<\/i>axis in a negative direction (down).<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nOnce you know about the quadrants in the coordinate plane, you can determine the quadrant of an ordered pair without even graphing it by looking at the chart above. Here\u2019s another way to think about it.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2011\/2017\/06\/07185244\/image009-1.jpg\" alt=\"Graph with quadrants. Quadrant 1 is positive, positive. Quadrant 2 is negative, positive. Quadrant 3 is negative, negative. Quadrant 4 is positive, negative.\" width=\"417\" height=\"378\" \/>\r\n\r\nThe example below details how to determine the quadrant location of a point just by thinking about the signs of its coordinates. Thinking about the quadrant location before plotting a point can help you prevent a mistake. It is also useful knowledge for checking that you have plotted a point correctly.\r\n<div class=\"bcc-box bcc-info\">\r\n<h3>Example<\/h3>\r\nIn which quadrant is the point [latex](\u22127,10)[\/latex] located?\r\n\r\n[reveal-answer q=\"222353\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"222353\"]\r\n\r\nLook at the signs of the <i>x-<\/i> and <i>y-<\/i>coordinates. For this ordered pair, the signs are [latex](\u2212,+)[\/latex].\r\n<p style=\"text-align: center\">[latex](\u22127,10)[\/latex]<\/p>\r\nUsing the table or grid above, locate the pattern [latex](\u2212,+)[\/latex].\r\n\r\nPoints with the pattern [latex](\u2212,+)[\/latex] are in Quadrant II.\r\n<h4>Answer<\/h4>\r\nThe point [latex](\u22127,10)[\/latex] is in Quadrant II.[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"bcc-box bcc-info\">\r\n<h3>Example<\/h3>\r\nIn which quadrant is the point [latex](\u221210,\u22125)[\/latex] located?\r\n\r\n[reveal-answer q=\"999799\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"999799\"]\r\n\r\nLook at the signs of the <i>x-<\/i> and <i>y-<\/i>coordinates. For this ordered pair, the signs are [latex](\u2212,\u2212)[\/latex].\r\n<p style=\"text-align: center\">[latex](\u221210,\u22125)[\/latex]<\/p>\r\nPoints with the pattern [latex](\u2212,\u2212)[\/latex] are in Quadrant III.\r\n\r\nUsing the table or grid above, locate the pattern [latex](\u2212,\u2212)[\/latex].\r\n<h4>Answer<\/h4>\r\nThe point [latex](\u221210,\u22125)[\/latex] is in Quadrant III.[\/hidden-answer]\r\n\r\n<\/div>\r\nWhat happens if an ordered pair has an <em>x<\/em>- or <i>y-<\/i>coordinate of zero? The example below shows the graph of the ordered pair [latex](0,4)[\/latex].\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2011\/2017\/06\/07185246\/image010-1.jpg\" alt=\"Graph of the point (0,4). The point is on the y-axis.\" width=\"417\" height=\"378\" \/>\r\n\r\nA point located on one of the axes is not considered to be in a quadrant. It is simply on one of the axes. Whenever the <i>x-<\/i>coordinate is 0, the point is located on the <i>y-<\/i>axis. Similarly, any point that has a <i>y-<\/i>coordinate of 0 will be located on the <i>x-<\/i>axis.\r\n<p id=\"video1\">Here are more examples of determining Quadrants:<\/p>\r\nhttps:\/\/youtu.be\/iTsJsPgcE4E\r\n<h2>Summary<\/h2>\r\nThe coordinate plane is a system for graphing and describing points and lines. The coordinate plane is comprised of a horizontal (<i>x<\/i>-) axis and a vertical (<i>y-<\/i>) axis. The intersection of these lines creates the origin, which is the point [latex](0,0)[\/latex]. The coordinate plane is split into four quadrants. Together, these features of the coordinate system allow for the graphical representation and communication about points, lines, and other algebraic concepts.","rendered":"<div class=\"bcc-box bcc-highlight\">\n<h3>Learning Objectives<\/h3>\n<ul>\n<li>Identify Quadrants on the Coordinate Plane\n<ul>\n<li>Identify the four quadrants of a coordinate plane<\/li>\n<li>Given an ordered pair, determine its quadrant<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/div>\n<h2 class=\"no-indent\" style=\"text-align: left\"><span style=\"color: #4a92c2\">Identify quadrants and use them to plot points<\/span><\/h2>\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 counter clockwise.<\/p>\n<p>Ordered pairs within any particular quadrant share certain characteristics. Look at each quadrant in the graph below. What do you notice about the signs of the <i>x-<\/i> and <i>y-<\/i>coordinates of the points within each quadrant?<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2011\/2017\/06\/07185241\/image008-1.jpg\" alt=\"A graph with many plotted points in different quadrants. Quadrant 1 has the point (1,3); the point (2,2); and the point (4,1). Quadrant 2 has the point negative 1, one; the point negative 2, 5; and the point negative 4, one. Quadrant 3 has the point negative 2, negative 3; the point negative 3, negative 3; and the point negative 1, negative 5. Quadrant 4 has the point 2, negative 1; the point 1, negative 3; and the point 4, negative 4.\" width=\"417\" height=\"378\" \/><\/p>\n<p>Within each quadrant, the signs of the <i>x-<\/i>coordinates and <i>y-<\/i>coordinates of each ordered pair are the same. They also follow a pattern, which is outlined in the table below.<\/p>\n<table>\n<thead>\n<tr>\n<th>Quadrant<\/th>\n<th>General Form of Point in this Quadrant<\/th>\n<th>Example<\/th>\n<th>Description<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>I<\/td>\n<td>[latex](+,+)[\/latex]<\/td>\n<td>[latex](5,4)[\/latex]<\/td>\n<td>Starting from the origin, go along the <i>x-<\/i>axis in a positive direction (right) and along the <i>y-<\/i>axis in a positive direction (up).<\/td>\n<\/tr>\n<tr>\n<td>II<\/td>\n<td>[latex](\u2212,+)[\/latex]<\/td>\n<td>[latex](\u22125,4)[\/latex]<\/td>\n<td>Starting from the origin, go along the <i>x-<\/i>axis in a negative direction (left) and along the <i>y-<\/i>axis in a positive direction (up).<\/td>\n<\/tr>\n<tr>\n<td>III<\/td>\n<td>[latex](\u2212,\u2212)[\/latex]<\/td>\n<td>[latex](\u22125,\u22124)[\/latex]<\/td>\n<td>Starting from the origin, go along the <i>x-<\/i>axis in a negative direction (left) and along the <i>y-<\/i>axis in a negative direction (down).<\/td>\n<\/tr>\n<tr>\n<td>IV<\/td>\n<td>[latex](+,\u2212)[\/latex]<\/td>\n<td>[latex](5,\u22124)[\/latex]<\/td>\n<td>Starting from the origin, go along the <i>x-<\/i>axis in a positive direction (right) and along the <i>y-<\/i>axis in a negative direction (down).<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Once you know about the quadrants in the coordinate plane, you can determine the quadrant of an ordered pair without even graphing it by looking at the chart above. Here\u2019s another way to think about it.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2011\/2017\/06\/07185244\/image009-1.jpg\" alt=\"Graph with quadrants. Quadrant 1 is positive, positive. Quadrant 2 is negative, positive. Quadrant 3 is negative, negative. Quadrant 4 is positive, negative.\" width=\"417\" height=\"378\" \/><\/p>\n<p>The example below details how to determine the quadrant location of a point just by thinking about the signs of its coordinates. Thinking about the quadrant location before plotting a point can help you prevent a mistake. It is also useful knowledge for checking that you have plotted a point correctly.<\/p>\n<div class=\"bcc-box bcc-info\">\n<h3>Example<\/h3>\n<p>In which quadrant is the point [latex](\u22127,10)[\/latex] located?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q222353\">Show Solution<\/span><\/p>\n<div id=\"q222353\" class=\"hidden-answer\" style=\"display: none\">\n<p>Look at the signs of the <i>x-<\/i> and <i>y-<\/i>coordinates. For this ordered pair, the signs are [latex](\u2212,+)[\/latex].<\/p>\n<p style=\"text-align: center\">[latex](\u22127,10)[\/latex]<\/p>\n<p>Using the table or grid above, locate the pattern [latex](\u2212,+)[\/latex].<\/p>\n<p>Points with the pattern [latex](\u2212,+)[\/latex] are in Quadrant II.<\/p>\n<h4>Answer<\/h4>\n<p>The point [latex](\u22127,10)[\/latex] is in Quadrant II.<\/p><\/div>\n<\/div>\n<\/div>\n<div class=\"bcc-box bcc-info\">\n<h3>Example<\/h3>\n<p>In which quadrant is the point [latex](\u221210,\u22125)[\/latex] located?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q999799\">Show Solution<\/span><\/p>\n<div id=\"q999799\" class=\"hidden-answer\" style=\"display: none\">\n<p>Look at the signs of the <i>x-<\/i> and <i>y-<\/i>coordinates. For this ordered pair, the signs are [latex](\u2212,\u2212)[\/latex].<\/p>\n<p style=\"text-align: center\">[latex](\u221210,\u22125)[\/latex]<\/p>\n<p>Points with the pattern [latex](\u2212,\u2212)[\/latex] are in Quadrant III.<\/p>\n<p>Using the table or grid above, locate the pattern [latex](\u2212,\u2212)[\/latex].<\/p>\n<h4>Answer<\/h4>\n<p>The point [latex](\u221210,\u22125)[\/latex] is in Quadrant III.<\/p><\/div>\n<\/div>\n<\/div>\n<p>What happens if an ordered pair has an <em>x<\/em>&#8211; or <i>y-<\/i>coordinate of zero? The example below shows the graph of the ordered pair [latex](0,4)[\/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\/2011\/2017\/06\/07185246\/image010-1.jpg\" alt=\"Graph of the point (0,4). The point is on the y-axis.\" width=\"417\" height=\"378\" \/><\/p>\n<p>A point located on one of the axes is not considered to be in a quadrant. It is simply on one of the axes. Whenever the <i>x-<\/i>coordinate is 0, the point is located on the <i>y-<\/i>axis. Similarly, any point that has a <i>y-<\/i>coordinate of 0 will be located on the <i>x-<\/i>axis.<\/p>\n<p id=\"video1\">Here are more examples of determining Quadrants:<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Identify the Quadrant of a Point on the Coordinate Plane\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/iTsJsPgcE4E?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<h2>Summary<\/h2>\n<p>The coordinate plane is a system for graphing and describing points and lines. The coordinate plane is comprised of a horizontal (<i>x<\/i>-) axis and a vertical (<i>y-<\/i>) axis. The intersection of these lines creates the origin, which is the point [latex](0,0)[\/latex]. The coordinate plane is split into four quadrants. Together, these features of the coordinate system allow for the graphical representation and communication about points, lines, and other algebraic concepts.<\/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-4605\">\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>Revision and Adaptation. <strong>Provided 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>Identify quadrants and use them to plot points. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com) . <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/iTsJsPgcE4E\">https:\/\/youtu.be\/iTsJsPgcE4E<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Unit 13: Graphing, from Developmental Math: An Open Program. <strong>Provided by<\/strong>: Monterey Institute of Technology. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/nrocnetwork.org\/dm-opentext\">http:\/\/nrocnetwork.org\/dm-opentext<\/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>\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":2,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Identify quadrants and use them to plot points\",\"author\":\"James Sousa (Mathispower4u.com) \",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/iTsJsPgcE4E\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Unit 13: Graphing, from Developmental Math: An Open Program\",\"author\":\"\",\"organization\":\"Monterey Institute of Technology\",\"url\":\"http:\/\/nrocnetwork.org\/dm-opentext\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"original\",\"description\":\"Revision and Adaptation\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"73f2961e-0767-4aff-b77d-14fcf5a6b6ba","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-4605","chapter","type-chapter","status-publish","hentry"],"part":4587,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/aacc-collegealgebrafoundations\/wp-json\/pressbooks\/v2\/chapters\/4605","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/aacc-collegealgebrafoundations\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/aacc-collegealgebrafoundations\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/aacc-collegealgebrafoundations\/wp-json\/wp\/v2\/users\/17533"}],"version-history":[{"count":2,"href":"https:\/\/courses.lumenlearning.com\/aacc-collegealgebrafoundations\/wp-json\/pressbooks\/v2\/chapters\/4605\/revisions"}],"predecessor-version":[{"id":5070,"href":"https:\/\/courses.lumenlearning.com\/aacc-collegealgebrafoundations\/wp-json\/pressbooks\/v2\/chapters\/4605\/revisions\/5070"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/aacc-collegealgebrafoundations\/wp-json\/pressbooks\/v2\/parts\/4587"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/aacc-collegealgebrafoundations\/wp-json\/pressbooks\/v2\/chapters\/4605\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/aacc-collegealgebrafoundations\/wp-json\/wp\/v2\/media?parent=4605"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/aacc-collegealgebrafoundations\/wp-json\/pressbooks\/v2\/chapter-type?post=4605"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/aacc-collegealgebrafoundations\/wp-json\/wp\/v2\/contributor?post=4605"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/aacc-collegealgebrafoundations\/wp-json\/wp\/v2\/license?post=4605"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}