{“appState”:{“pageLoadApiCallsStatus”:true},”articleState”:{“article”:{“headers”:{“creationTime”:”2016-03-26T18:31:57+00:00″,”modifiedTime”:”2016-03-26T18:31:57+00:00″,”timestamp”:”2022-09-14T18:08:02+00:00″},”data”:{“breadcrumbs”:[{“name”:”Academics & The Arts”,”_links”:{“self”:”https://dummies-api.dummies.com/v2/categories/33662″},”slug”:”academics-the-arts”,”categoryId”:33662},{“name”:”Math”,”_links”:{“self”:”https://dummies-api.dummies.com/v2/categories/33720″},”slug”:”math”,”categoryId”:33720},{“name”:”Calculus”,”_links”:{“self”:”https://dummies-api.dummies.com/v2/categories/33723″},”slug”:”calculus”,”categoryId”:33723}],”title”:”Drawing with 3-D Cartesian Coordinates”,”strippedTitle”:”drawing with 3-d cartesian coordinates”,”slug”:”drawing-with-3-d-cartesian-coordinates”,”canonicalUrl”:””,”seo”:{“metaDescription”:”The three-dimensional (3-D) Cartesian coordinate system (also called 3-D rectangular coordinates) is the natural extension of the 2-D Cartesian graph. The key d”,”noIndex”:0,”noFollow”:0},”content”:”<p>The three-dimensional (3-D) Cartesian coordinate system (also called 3-D rectangular coordinates) is the natural extension of the 2-D Cartesian graph. The key difference is the addition of a third axis, the <i>z</i>-axis, extending perpendicularly through the origin.</p>\n<div class=\”imageBlock\” style=\”width:360px;\”><img src=\”https://www.dummies.com/wp-content/uploads/312189.image0.jpg\” width=\”360\” height=\”310\” alt=\”The first octant of the 3-D Cartesian coordinate system.\”/><div class=\”imageCaption\”>The first octant of the 3-D Cartesian coordinate system.</div></div>\n<p>Drawing a 3-D graph in two dimensions is kind of tricky. To get a better sense about how to think in 3-D, hold up the figure where you can compare it with the interior corner of a room (not a round room!). Note the following:</p>\n<ul class=\”level-one\”>\n <li><p class=\”first-para\”>The <i>x</i>-axis corresponds to where the left-hand wall meets the floor. </p>\n </li>\n <li><p class=\”first-para\”>The <i>y</i>-axis corresponds to where the right-hand wall meets the floor.</p>\n </li>\n <li><p class=\”first-para\”>The <i>z</i>-axis corresponds to where the two walls meet.</p>\n </li>\n</ul>\n<p>Just as the 2-D Cartesian graph is divided into four quadrants, the 3-D graph is divided into eight <i>octants.</i> From your perspective as you look at the graph, you’re standing inside the first octant, where all values of <i>x</i>, <i>y</i>, and <i>z</i> are positive.</p>\n<div class=\”imageBlock\” style=\”width:360px;\”><img src=\”https://www.dummies.com/wp-content/uploads/312190.image1.jpg\” width=\”360\” height=\”351\” alt=\”Plotting the point (1, 2, 5) on the 3-D Cartesian coordinate system.\”/><div class=\”imageCaption\”>Plotting the point (1, 2, 5) on the 3-D Cartesian coordinate system.</div></div>\n<p>The figure above shows the complete 3-D Cartesian system with the point (1, 2, 5) plotted. In similarity with regular Cartesian coordinates, you plot this point by counting 1 unit in the positive <i>x</i> direction, and then 2 units in the positive <i>y</i> direction, and finally 5 units in the positive <i>z</i> direction.</p>”,”description”:”<p>The three-dimensional (3-D) Cartesian coordinate system (also called 3-D rectangular coordinates) is the natural extension of the 2-D Cartesian graph. The key difference is the addition of a third axis, the <i>z</i>-axis, extending perpendicularly through the origin.</p>\n<div class=\”imageBlock\” style=\”width:360px;\”><img src=\”https://www.dummies.com/wp-content/uploads/312189.image0.jpg\” width=\”360\” height=\”310\” alt=\”The first octant of the 3-D Cartesian coordinate system.\”/><div class=\”imageCaption\”>The first octant of the 3-D Cartesian coordinate system.</div></div>\n<p>Drawing a 3-D graph in two dimensions is kind of tricky. To get a better sense about how to think in 3-D, hold up the figure where you can compare it with the interior corner of a room (not a round room!). Note the following:</p>\n<ul class=\”level-one\”>\n <li><p class=\”first-para\”>The <i>x</i>-axis corresponds to where the left-hand wall meets the floor. </p>\n </li>\n <li><p class=\”first-para\”>The <i>y</i>-axis corresponds to where the right-hand wall meets the floor.</p>\n </li>\n <li><p class=\”first-para\”>The <i>z</i>-axis corresponds to where the two walls meet.</p>\n </li>\n</ul>\n<p>Just as the 2-D Cartesian graph is divided into four quadrants, the 3-D graph is divided into eight <i>octants.</i> From your perspective as you look at the graph, you’re standing inside the first octant, where all values of <i>x</i>, <i>y</i>, and <i>z</i> are positive.</p>\n<div class=\”imageBlock\” style=\”width:360px;\”><img src=\”https://www.dummies.com/wp-content/uploads/312190.image1.jpg\” width=\”360\” height=\”351\” alt=\”Plotting the point (1, 2, 5) on the 3-D Cartesian coordinate system.\”/><div class=\”imageCaption\”>Plotting the point (1, 2, 5) on the 3-D Cartesian coordinate system.</div></div>\n<p>The figure above shows the complete 3-D Cartesian system with the point (1, 2, 5) plotted. In similarity with regular Cartesian coordinates, you plot this point by counting 1 unit in the positive <i>x</i> direction, and then 2 units in the positive <i>y</i> direction, and finally 5 units in the positive <i>z</i> direction.</p>”,”blurb”:””,”authors”:[{“authorId”:9399,”name”:”Mark Zegarelli”,”slug”:”mark-zegarelli”,”description”:” <b>Mark Zegarelli</b> is a professional writer with degrees in both English and Math from Rutgers University. He has earned his living for many years writing vast quantities of logic puzzles, a hefty chunk of software documentation, and the occasional book or film review. Along the way, he&#8217;s also paid a few bills doing housecleaning, decorative painting, and (for ten hours) retail sales. 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