{"id":85,"date":"2023-06-21T13:22:31","date_gmt":"2023-06-21T13:22:31","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/chapter\/summary-points-and-lines-in-the-plane\/"},"modified":"2023-07-03T19:15:43","modified_gmt":"2023-07-03T19:15:43","slug":"summary-points-and-lines-in-the-plane","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/chapter\/summary-points-and-lines-in-the-plane\/","title":{"raw":"Summary: Points and Lines in the Coordinate Plane","rendered":"Summary: Points and Lines in the Coordinate Plane"},"content":{"raw":"\n\n<div>\n<div>\n<h2>Key Concepts<\/h2>\n<\/div>\n<ul>\n \t<li>We can locate or plot points in the Cartesian coordinate system using ordered pairs which are defined as displacement from the <em>x-<\/em>axis and displacement from the <em>y-<\/em>axis.<\/li>\n \t<li>An equation can be graphed in the plane by creating a table of values and plotting points.<\/li>\n \t<li>Using a graphing calculator or a computer program makes graphing equations faster and more accurate. Equations usually have to be entered in the form <em>y=<\/em>_____.<\/li>\n \t<li>Finding the <em>x- <\/em>and <em>y-<\/em>intercepts can define the graph of a line. These are the points where the graph crosses the axes.<\/li>\n \t<li>The distance formula is derived from the Pythagorean Theorem and is used to find the length of a line segment.<\/li>\n \t<li>The midpoint formula provides a method of finding the coordinates of the midpoint by dividing the sum of the <em>x<\/em>-coordinates and the sum of the <em>y<\/em>-coordinates of the endpoints by 2.<\/li>\n<\/ul>\n<h2>Glossary<\/h2>\n<dl id=\"fs-id1165131990658\" class=\"definition\">\n \t<dt><strong>Cartesian coordinate system<\/strong><\/dt>\n \t<dd id=\"fs-id1165131990661\">a grid system designed with perpendicular axes invented by Ren\u00e9 Descartes<\/dd>\n<\/dl>\n<dl id=\"fs-id1165132943522\" class=\"definition\">\n \t<dt><strong>equation in two variables<\/strong><\/dt>\n \t<dd id=\"fs-id1165132943525\">a mathematical statement, typically written in <em>x <\/em>and <em>y<\/em>, in which two expressions are equal<\/dd>\n<\/dl>\n<dl id=\"fs-id1165132943528\" class=\"definition\">\n \t<dt><strong>distance formula<\/strong><\/dt>\n \t<dd id=\"fs-id1165134297639\">a formula that can be used to find the length of a line segment if the endpoints are known<\/dd>\n<\/dl>\n<dl id=\"fs-id1165134297646\" class=\"definition\">\n \t<dt><strong>graph in two variables<\/strong><\/dt>\n \t<dd id=\"fs-id1165135486042\">the graph of an equation in two variables, which is always shown in two variables in the two-dimensional plane<\/dd>\n<\/dl>\n<dl id=\"fs-id1165137644987\" class=\"definition\">\n \t<dt><strong>intercepts<\/strong><\/dt>\n \t<dd id=\"fs-id1165137644990\">the points at which the graph of an equation crosses the <em>x<\/em>-axis and the <em>y<\/em>-axis<\/dd>\n<\/dl>\n<dl id=\"fs-id1165132943528\" class=\"definition\">\n \t<dt><strong>midpoint formula<\/strong><\/dt>\n \t<dd id=\"fs-id1165134297639\">&nbsp;a formula to find the point that divides a line segment into two parts of equal length<\/dd>\n<\/dl>\n<dl id=\"fs-id1165132943528\" class=\"definition\">\n \t<dt><strong>ordered pair<\/strong><\/dt>\n \t<dd id=\"fs-id1165134297639\">a pair of numbers indicating horizontal displacement and vertical displacement from the origin; also known as a coordinate pair, [latex]\\left(x,y\\right)[\/latex]<\/dd>\n<\/dl>\n<dl id=\"fs-id1165134297646\" class=\"definition\">\n \t<dt><strong>origin<\/strong><\/dt>\n \t<dd id=\"fs-id1165135486042\">the point where the two axes cross in the center of the plane, described by the ordered pair [latex]\\left(0,0\\right)[\/latex]<\/dd>\n<\/dl>\n<dl id=\"fs-id1165137644987\" class=\"definition\">\n \t<dt><strong>quadrant<\/strong><\/dt>\n \t<dd id=\"fs-id1165137644990\">one quarter of the coordinate plane, created when the axes divide the plane into four sections<\/dd>\n<\/dl>\n<dl id=\"fs-id1165134297646\" class=\"definition\">\n \t<dt><strong><em>x<\/em>-axis<\/strong><\/dt>\n \t<dd id=\"fs-id1165135486042\">the common name of the horizontal axis on a coordinate plane; a number line increasing from left to right<\/dd>\n<\/dl>\n<dl id=\"fs-id1165137644987\" class=\"definition\">\n \t<dt><strong><em>x-<\/em>coordinate<\/strong><\/dt>\n \t<dd id=\"fs-id1165137644990\">the first coordinate of an ordered pair, representing the horizontal displacement and direction from the origin<\/dd>\n<\/dl>\n<dl id=\"fs-id1165134297646\" class=\"definition\">\n \t<dt><strong><em>x-<\/em>intercept<\/strong><\/dt>\n \t<dd id=\"fs-id1165135486042\">the point where a graph intersects the <em>x-<\/em>axis; an ordered pair with a <em>y<\/em>-coordinate of zero<\/dd>\n<\/dl>\n<dl id=\"fs-id1165137644987\" class=\"definition\">\n \t<dt><strong><em>y<\/em>-axis<\/strong><\/dt>\n \t<dd id=\"fs-id1165137644990\">the common name of the vertical axis on a coordinate plane; a number line increasing from bottom to top<\/dd>\n<\/dl>\n<dl id=\"fs-id1165134297646\" class=\"definition\">\n \t<dt><strong><em>y-<\/em>coordinate<\/strong><\/dt>\n \t<dd id=\"fs-id1165135486042\">&nbsp;the second coordinate of an ordered pair, representing the vertical displacement and direction from the origin<\/dd>\n<\/dl>\n<dl id=\"fs-id1165137644987\" class=\"definition\">\n \t<dt><strong><em>y<\/em>-intercept<\/strong><\/dt>\n \t<dd id=\"fs-id1165137644990\">a point where a graph intercepts the <em>y-<\/em>axis; an ordered pair with an <em>x<\/em>-coordinate of zero<\/dd>\n<\/dl>\n<\/div>\n\n","rendered":"<div>\n<div>\n<h2>Key Concepts<\/h2>\n<\/div>\n<ul>\n<li>We can locate or plot points in the Cartesian coordinate system using ordered pairs which are defined as displacement from the <em>x-<\/em>axis and displacement from the <em>y-<\/em>axis.<\/li>\n<li>An equation can be graphed in the plane by creating a table of values and plotting points.<\/li>\n<li>Using a graphing calculator or a computer program makes graphing equations faster and more accurate. Equations usually have to be entered in the form <em>y=<\/em>_____.<\/li>\n<li>Finding the <em>x- <\/em>and <em>y-<\/em>intercepts can define the graph of a line. These are the points where the graph crosses the axes.<\/li>\n<li>The distance formula is derived from the Pythagorean Theorem and is used to find the length of a line segment.<\/li>\n<li>The midpoint formula provides a method of finding the coordinates of the midpoint by dividing the sum of the <em>x<\/em>-coordinates and the sum of the <em>y<\/em>-coordinates of the endpoints by 2.<\/li>\n<\/ul>\n<h2>Glossary<\/h2>\n<dl id=\"fs-id1165131990658\" class=\"definition\">\n<dt><strong>Cartesian coordinate system<\/strong><\/dt>\n<dd id=\"fs-id1165131990661\">a grid system designed with perpendicular axes invented by Ren\u00e9 Descartes<\/dd>\n<\/dl>\n<dl id=\"fs-id1165132943522\" class=\"definition\">\n<dt><strong>equation in two variables<\/strong><\/dt>\n<dd id=\"fs-id1165132943525\">a mathematical statement, typically written in <em>x <\/em>and <em>y<\/em>, in which two expressions are equal<\/dd>\n<\/dl>\n<dl id=\"fs-id1165132943528\" class=\"definition\">\n<dt><strong>distance formula<\/strong><\/dt>\n<dd id=\"fs-id1165134297639\">a formula that can be used to find the length of a line segment if the endpoints are known<\/dd>\n<\/dl>\n<dl id=\"fs-id1165134297646\" class=\"definition\">\n<dt><strong>graph in two variables<\/strong><\/dt>\n<dd id=\"fs-id1165135486042\">the graph of an equation in two variables, which is always shown in two variables in the two-dimensional plane<\/dd>\n<\/dl>\n<dl id=\"fs-id1165137644987\" class=\"definition\">\n<dt><strong>intercepts<\/strong><\/dt>\n<dd id=\"fs-id1165137644990\">the points at which the graph of an equation crosses the <em>x<\/em>-axis and the <em>y<\/em>-axis<\/dd>\n<\/dl>\n<dl id=\"fs-id1165132943528\" class=\"definition\">\n<dt><strong>midpoint formula<\/strong><\/dt>\n<dd id=\"fs-id1165134297639\">&nbsp;a formula to find the point that divides a line segment into two parts of equal length<\/dd>\n<\/dl>\n<dl id=\"fs-id1165132943528\" class=\"definition\">\n<dt><strong>ordered pair<\/strong><\/dt>\n<dd id=\"fs-id1165134297639\">a pair of numbers indicating horizontal displacement and vertical displacement from the origin; also known as a coordinate pair, [latex]\\left(x,y\\right)[\/latex]<\/dd>\n<\/dl>\n<dl id=\"fs-id1165134297646\" class=\"definition\">\n<dt><strong>origin<\/strong><\/dt>\n<dd id=\"fs-id1165135486042\">the point where the two axes cross in the center of the plane, described by the ordered pair [latex]\\left(0,0\\right)[\/latex]<\/dd>\n<\/dl>\n<dl id=\"fs-id1165137644987\" class=\"definition\">\n<dt><strong>quadrant<\/strong><\/dt>\n<dd id=\"fs-id1165137644990\">one quarter of the coordinate plane, created when the axes divide the plane into four sections<\/dd>\n<\/dl>\n<dl id=\"fs-id1165134297646\" class=\"definition\">\n<dt><strong><em>x<\/em>-axis<\/strong><\/dt>\n<dd id=\"fs-id1165135486042\">the common name of the horizontal axis on a coordinate plane; a number line increasing from left to right<\/dd>\n<\/dl>\n<dl id=\"fs-id1165137644987\" class=\"definition\">\n<dt><strong><em>x-<\/em>coordinate<\/strong><\/dt>\n<dd id=\"fs-id1165137644990\">the first coordinate of an ordered pair, representing the horizontal displacement and direction from the origin<\/dd>\n<\/dl>\n<dl id=\"fs-id1165134297646\" class=\"definition\">\n<dt><strong><em>x-<\/em>intercept<\/strong><\/dt>\n<dd id=\"fs-id1165135486042\">the point where a graph intersects the <em>x-<\/em>axis; an ordered pair with a <em>y<\/em>-coordinate of zero<\/dd>\n<\/dl>\n<dl id=\"fs-id1165137644987\" class=\"definition\">\n<dt><strong><em>y<\/em>-axis<\/strong><\/dt>\n<dd id=\"fs-id1165137644990\">the common name of the vertical axis on a coordinate plane; a number line increasing from bottom to top<\/dd>\n<\/dl>\n<dl id=\"fs-id1165134297646\" class=\"definition\">\n<dt><strong><em>y-<\/em>coordinate<\/strong><\/dt>\n<dd id=\"fs-id1165135486042\">&nbsp;the second coordinate of an ordered pair, representing the vertical displacement and direction from the origin<\/dd>\n<\/dl>\n<dl id=\"fs-id1165137644987\" class=\"definition\">\n<dt><strong><em>y<\/em>-intercept<\/strong><\/dt>\n<dd id=\"fs-id1165137644990\">a point where a graph intercepts the <em>y-<\/em>axis; an ordered pair with an <em>x<\/em>-coordinate of zero<\/dd>\n<\/dl>\n<\/div>\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-85\">\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>College Algebra. <strong>Authored by<\/strong>: Abramson, Jay et al.. <strong>Provided by<\/strong>: OpenStax. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@5.2\">http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@5.2<\/a>. <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\/9b08c294-057f-4201-9f48-5d6ad992740d@5.2<\/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":395986,"menu_order":21,"template":"","meta":{"_candela_citation":"[{\"type\":\"original\",\"description\":\"Revision and Adaptation\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"College Algebra\",\"author\":\"Abramson, Jay et al.\",\"organization\":\"OpenStax\",\"url\":\"http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@5.2\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@5.2\"}]","CANDELA_OUTCOMES_GUID":"8d9c3cf2-8f8e-44d1-8904-352924d11dd2","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-85","chapter","type-chapter","status-publish","hentry"],"part":115,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/85","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/wp\/v2\/users\/395986"}],"version-history":[{"count":1,"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/85\/revisions"}],"predecessor-version":[{"id":495,"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/85\/revisions\/495"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/parts\/115"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/85\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/wp\/v2\/media?parent=85"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=85"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/wp\/v2\/contributor?post=85"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/wp\/v2\/license?post=85"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}