{"id":58244,"date":"2020-01-16T16:54:55","date_gmt":"2020-01-16T16:54:55","guid":{"rendered":"https:\/\/www.mometrix.com\/academy\/?page_id=58244"},"modified":"2026-03-28T10:58:45","modified_gmt":"2026-03-28T15:58:45","slug":"calculations-using-points-on-a-graph","status":"publish","type":"page","link":"https:\/\/www.mometrix.com\/academy\/calculations-using-points-on-a-graph\/","title":{"rendered":"Calculations Using Points on a Graph"},"content":{"rendered":"\n\t\t\t<div id=\"mmDeferVideoEncompass_VRoPHU1-Oyw\" style=\"position: relative;\">\n\t\t\t<picture>\n\t\t\t\t<source srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.webp\" type=\"image\/webp\">\n\t\t\t\t<source srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" type=\"image\/jpeg\"> \n\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" loading=\"eager\" id=\"videoThumbnailImage_VRoPHU1-Oyw\" data-source-videoID=\"VRoPHU1-Oyw\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" alt=\"Calculations Using Points on a Graph Video\" height=\"464\" width=\"825\" class=\"size-full\" data-matomo-title = \"Calculations Using Points on a Graph\">\n\t\t\t<\/picture>\n\t\t\t<\/div>\n\t\t\t<style>img#videoThumbnailImage_VRoPHU1-Oyw:hover {cursor:pointer;} img#videoThumbnailImage_VRoPHU1-Oyw {background-size:contain;background-image:url(\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/365-calculations-using-points-on-a-graph-2-1.webp\");}<\/style>\n\t\t\t<script defer>\n\t\t\t  jQuery(\"img#videoThumbnailImage_VRoPHU1-Oyw\").click(function() {\n\t\t\t\tlet videoId = jQuery(this).attr(\"data-source-videoID\");\n\t\t\t\tlet helpTag = '<div id=\"mmDeferVideoYTMessage_VRoPHU1-Oyw\" style=\"display: none;position: absolute;top: -24px;width: 100%;text-align: center;\"><span style=\"font-style: italic;font-size: small;border-top: 1px solid #fc0;\">Having trouble? <a href=\"https:\/\/www.youtube.com\/watch?v='+videoId+'\" target=\"_blank\">Click here to watch on YouTube.<\/a><\/span><\/div>';\n\t\t\t\tlet tag = document.createElement(\"iframe\");\n\t\t\t\ttag.id = \"yt\" + videoId;\n\t\t\t\ttag.src = \"https:\/\/www.youtube-nocookie.com\/embed\/\" + videoId + \"?autoplay=1&controls=1&wmode=opaque&rel=0&egm=0&iv_load_policy=3&hd=0&enablejsapi=1\";\n\t\t\t\ttag.frameborder = 0;\n\t\t\t\ttag.allow = \"autoplay; fullscreen\";\n\t\t\t\ttag.width = this.width;\n\t\t\t\ttag.height = this.height;\n\t\t\t\ttag.setAttribute(\"data-matomo-title\",\"Calculations Using Points on a Graph\");\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_VRoPHU1-Oyw\").html(tag);\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_VRoPHU1-Oyw\").prepend(helpTag);\n\t\t\t\tsetTimeout(function(){jQuery(\"div#mmDeferVideoYTMessage_VRoPHU1-Oyw\").css(\"display\", \"block\");}, 2000);\n\t\t\t  });\n\t\t\t  \n\t\t\t<\/script>\n\t\t\n<p><script>\nfunction CSE_Function() {\n  var x = document.getElementById(\"CSE\");\n  if (x.style.display === \"none\") {\n    x.style.display = \"block\";\n  } else {\n    x.style.display = \"none\";\n  }\n}\n<\/script><\/p>\n<div class=\"moc-toc hide-on-desktop hide-on-tablet\">\n<div><button onclick=\"CSE_Function()\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/12\/toc2.svg\" width=\"16\" height=\"16\" alt=\"show or hide table of contents\"><\/button><\/p>\n<p>On this page<\/p>\n<\/div>\n<nav id=\"CSE\" style=\"display:none;\">\n<ul>\n<li class=\"toc-h2\"><a href=\"#Plotting_a_Point\" class=\"smooth-scroll\">Plotting a Point<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Distance_Formula\" class=\"smooth-scroll\">Distance Formula<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Midpoint_Formula\" class=\"smooth-scroll\">Midpoint Formula<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Graph_Practice_Questions\" class=\"smooth-scroll\">Graph Practice Questions<\/a><\/li>\n<\/ul>\n<\/nav>\n<\/div>\n<div class=\"accordion\"><input id=\"transcript\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"transcript\">Transcript<\/label><input id=\"PQs\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQs\">Practice<\/label>\n<div class=\"spoiler\" id=\"transcript-spoiler\">\n<p>Hello and welcome to this video about calculations using points on the coordinate plane! <\/p>\n<p>So first off, let\u2019s remember that a one-dimensional number line is a representation of all real numbers that extends infinitely in both the positive and negative directions and looks something like this:<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/07\/number-line.png\" alt=\"\" width=\"543\" height=\"76.5\" class=\"aligncenter size-full wp-image-87133\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/07\/number-line.png 1086w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/07\/number-line-300x42.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/07\/number-line-1024x144.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/07\/number-line-768x108.png 768w\" sizes=\"(max-width: 1086px) 100vw, 1086px\" \/><\/p>\n<p>When two number lines intersect at a right angle at their 0 coordinates, the two-dimensional coordinate plane is formed, which typically looks something like this:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/07\/coordinate-plane.jpg\" alt=\"\" width=\"448\" height=\"436\" class=\"aligncenter size-full wp-image-87136\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/07\/coordinate-plane.jpg 896w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/07\/coordinate-plane-300x292.jpg 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/07\/coordinate-plane-768x747.jpg 768w\" sizes=\"auto, (max-width: 448px) 100vw, 448px\" \/><\/p>\n<p>Generally, the horizontal axis is called the \\(x\\)-axis and the vertical axis is called the \\(y\\)-axis. The point where the axes intersect is called the <strong>origin<\/strong>. <\/p>\n<h2><span id=\"Plotting_a_Point\" class=\"m-toc-anchor\"><\/span>Plotting a Point<\/h2>\n<p>\nLet\u2019s <a href=\"https:\/\/www.mometrix.com\/academy\/cartesian-coordinate-plane-and-graphing\/\" class=\"ylist\">plot<\/a> a point on the coordinate plane.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/07\/coordinate-plane-point-A.jpg\" alt=\"\" width=\"449\" height=\"440\" class=\"aligncenter size-full wp-image-87142\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/07\/coordinate-plane-point-A.jpg 898w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/07\/coordinate-plane-point-A-300x294.jpg 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/07\/coordinate-plane-point-A-768x753.jpg 768w\" sizes=\"auto, (max-width: 449px) 100vw, 449px\" \/><\/p>\n<p>The location of Point A is given as a horizontal component (\\(x\\)) and a vertical component (<em>y<\/em>) and written as \\((x,y)\\). From the origin, to get to Point A, we would count two units to the right and three units up. So, the coordinates of Point A are \\((2,3)\\). Likewise, the coordinates of the origin are \\((0,0)\\).<\/p>\n<h3><span id=\"Zooming_In_or_Out\" class=\"m-toc-anchor\"><\/span>Zooming In or Out<\/h3>\n<p>\nSince the coordinate plane is comprised of number lines, they can be viewed \u201czoomed in\u201d or \u201czoomed out\u201d as much as necessary to convey data or a story. For example, the \\(x\\)-axis here has been \u201czoomed in\u201d:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/07\/coordinate-plane-point-B.jpg\" alt=\"\" width=\"443\" height=\"439\" class=\"aligncenter size-full wp-image-87145\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/07\/coordinate-plane-point-B.jpg 886w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/07\/coordinate-plane-point-B-300x297.jpg 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/07\/coordinate-plane-point-B-150x150.jpg 150w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/07\/coordinate-plane-point-B-768x761.jpg 768w\" sizes=\"auto, (max-width: 443px) 100vw, 443px\" \/><\/p>\n<p>Because of the scale of the \\(x\\)-axis, the coordinate points of Point B are \\((\\frac{1}{2},3)\\).<\/p>\n<p>And the \\(x\\)-axis has been zoomed in here, while the \\(y\\)-axis has been zoomed out:<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/07\/coordinate-plane-point-C.jpg\" alt=\"\" width=\"449.5\" height=\"439.5\" class=\"aligncenter size-full wp-image-87148\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/07\/coordinate-plane-point-C.jpg 899w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/07\/coordinate-plane-point-C-300x293.jpg 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/07\/coordinate-plane-point-C-768x751.jpg 768w\" sizes=\"(max-width: 899px) 100vw, 899px\" \/><\/p>\n<p>Because of the scales of the axes, the coordinates of Point C are \\((0.2,300)\\).<\/p>\n<h2><span id=\"Distance_Formula\" class=\"m-toc-anchor\"><\/span>Distance Formula<\/h2>\n<p>\nUsing the coordinates of points on a coordinate plane, we can calculate the distance between two points.<\/p>\n<p>The <strong>distance formula<\/strong> (an application of the <a href=\"https:\/\/www.mometrix.com\/academy\/pythagorean-theorem\/\" class=\"ylist\">Pythagorean theorem<\/a>) looks like this:<\/p>\n<div class=\"examplesentence\">\\(D=\\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\)<\/div>\n<p>&nbsp;<\/p>\n<p>In words, it\u2019s \u201cthe square root of the horizontal distance squared plus the vertical distance squared.\u201d<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/07\/coordinate-plane-points-D-and-A.jpg\" alt=\"\" width=\"458.4\" height=\"454.8\" class=\"aligncenter size-full wp-image-87151\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/07\/coordinate-plane-points-D-and-A.jpg 762w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/07\/coordinate-plane-points-D-and-A-300x298.jpg 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/07\/coordinate-plane-points-D-and-A-150x150.jpg 150w\" sizes=\"(max-width: 762px) 100vw, 762px\" \/><\/p>\n<p>In this case, the formula can be used, but since Points A and D lie on the same horizontal gridline, all we need to do is count squares (this also works for two points on the same vertical gridline). The distance from Point A to Point D is 6 because the two points are 6 squares apart.<\/p>\n<p>Using the formula yields the same result:<\/p>\n<div class=\"examplesentence\">\n\\(D=\\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\)&nbsp;<br \/>\n\\(D=\\sqrt{(2-(-4))^2+(3-3)^2}\\)&nbsp;<br \/>\n\\(D=\\sqrt{(6)^2+(0)^2}\\)&nbsp;<br \/>\n\\(D=\\sqrt{36+0}\\)&nbsp;<br \/>\n\\(D=\\sqrt{36}\\)&nbsp;<br \/>\n\\(D=6\\)\n<\/div>\n<p>\n&nbsp;<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/07\/coordinate-plane-points-B-and-E.jpg\" alt=\"\" width=\"461.4\" height=\"454.8\" class=\"aligncenter size-full wp-image-87154\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/07\/coordinate-plane-points-B-and-E.jpg 769w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/07\/coordinate-plane-points-B-and-E-300x296.jpg 300w\" sizes=\"(max-width: 769px) 100vw, 769px\" \/> <\/p>\n<p>In this case, we can see that the coordinates of Point B are \\((\\frac{1}{2},3)\\) and the coordinates of Point E are \\((\\frac{3}{2},-6)\\). In order to determine the distance between the two points, we\u2019ll need to use the formula because the points do not share a gridline, so we can\u2019t simply count squares to determine the distance.<\/p>\n<div class=\"examplesentence\">\n\\(D=\\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\)&nbsp;<br \/>\n\\(D=\\sqrt{(\\frac{3}{2}-\\frac{1}{2})^2+(-6-3)^2}\\)&nbsp;<br \/>\n\\(D=\\sqrt{((1)^2+(-9)^2}\\)&nbsp;<br \/>\n\\(D=\\sqrt{1+81}\\)&nbsp;<br \/>\n\\(D=\\sqrt{82}\\)&nbsp;<br \/>\n\\(D\u22489.055\\)\n<\/div>\n<p>\n&nbsp;<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/07\/coordinate-plane-points-C-and-F.jpg\" alt=\"\" width=\"461.4\" height=\"455.4\" class=\"aligncenter size-full wp-image-87157\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/07\/coordinate-plane-points-C-and-F.jpg 769w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/07\/coordinate-plane-points-C-and-F-300x296.jpg 300w\" sizes=\"(max-width: 769px) 100vw, 769px\" \/><\/p>\n<p>In this case, we\u2019re going to need to <a href=\"https:\/\/www.mometrix.com\/academy\/rounding\/\" class=\"ylist\">estimate<\/a> the coordinates of Point F because it doesn\u2019t lie at the intersection of two gridlines. It is often the case that we need to estimate the coordinates of a point. Let\u2019s estimate Point F to be located at \\((-0.4,-350)\\). Now, let\u2019s use the distance formula to get a good idea of the distance between Points C and F:<\/p>\n<div class=\"examplesentence longmath-container\">\n\\(D=\\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\)<br \/>\n\\(D=\\sqrt{(-0.4-0.2)^2+(-350-300)^2}\\)<br \/>\n\\(D=\\sqrt{(-0.6)^2+(-650)^2}\\)<br \/>\n\\(D=\\sqrt{0.36+422,500}\\)<br \/>\n\\(D=\\sqrt{422,500.36}\\)<br \/>\n\\(D\u2248650\\)\n<\/div>\n<p>\n&nbsp;<br \/>\nUsing the coordinates of points on a coordinate plane, we can also calculate the coordinates of a point that lies exactly halfway between two points, which is known as the midpoint.<\/p>\n<h2><span id=\"Midpoint_Formula\" class=\"m-toc-anchor\"><\/span>Midpoint Formula<\/h2>\n<p>\nThe formula for finding the <strong>midpoint<\/strong> coordinates looks like this:<\/p>\n<div class=\"examplesentence\">\\(M=(\\frac{x_1+x_2}{2},\\frac{y_1+y_2}{2})\\)<\/div>\n<p>\n&nbsp;<br \/>\nIn words, it\u2019s easy to remember as \u201cthe average of the \\(x\\)\u2019s, the average of the \\(y\\)\u2019s.\u201d <\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/07\/coordinate-plane-points-D-and-A-blue.jpg\" alt=\"\" width=\"525.75\" height=\"511.5\" class=\"aligncenter size-full wp-image-87160\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/07\/coordinate-plane-points-D-and-A-blue.jpg 701w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/07\/coordinate-plane-points-D-and-A-blue-300x292.jpg 300w\" sizes=\"(max-width: 701px) 100vw, 701px\" \/><\/p>\n<p>As we saw previously, the distance between Points A and D is 6. Half of that distance is 3. Since Points A and D lie on the same gridline, the midpoint will lie there as well, at the coordinates \\((-1,3)\\).<\/p>\n<p>We can verify this with the formula:<\/p>\n<div class=\"examplesentence\">\n\\(M=(\\frac{x_1+x_2}{2},\\frac{y_1+y_2}{2})\\)&nbsp;<br \/>\n\\(M=(\\frac{-4+2}{2},\\frac{3+3}{2})\\)&nbsp;<br \/>\n\\(M=(\\frac{-2}{2},\\frac{6}{2})\\)&nbsp;<br \/>\n\\(M=(-1,3)\\)\n<\/div>\n<p>\n&nbsp;<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/07\/coordinate-plane-points-B-and-E-blue.jpg\" alt=\"\" width=\"528.75\" height=\"516.75\" class=\"aligncenter size-full wp-image-87163\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/07\/coordinate-plane-points-B-and-E-blue.jpg 705w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/07\/coordinate-plane-points-B-and-E-blue-300x293.jpg 300w\" sizes=\"(max-width: 705px) 100vw, 705px\" \/><\/p>\n<p>Even though we can always calculate half of the distance between two points, that won\u2019t tell us the coordinates of the midpoint in this example like the formula does: <\/p>\n<div class=\"examplesentence\">\n\\(M=(\\frac{x_1+x_2}{2},\\frac{y_1+y_2}{2})\\)&nbsp;<br \/>\n\\(M=(\\frac{\\frac{1}{2}+\\frac{3}{2}}{2},\\frac{3+(-6)}{2})\\)&nbsp;<br \/>\n\\(M=(\\frac{2}{2},\\frac{-3}{2})\\)&nbsp;<br \/>\n\\(M=(1,-\\frac{3}{2})\\)\n<\/div>\n<p>\n&nbsp;<br \/>\nTo graph, we\u2019ll need to estimate the location of \\(-\\frac{3}{2}\\).<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/07\/coordinate-plane-points-C-and-F-blue.jpg\" alt=\"\" width=\"528.75\" height=\"516.75\" class=\"aligncenter size-full wp-image-87166\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/07\/coordinate-plane-points-C-and-F-blue.jpg 705w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/07\/coordinate-plane-points-C-and-F-blue-300x293.jpg 300w\" sizes=\"(max-width: 705px) 100vw, 705px\" \/> <\/p>\n<p>Previously, we estimated the coordinates of Point F to be \\((-0.4,-350)\\). Let\u2019s use the formula to estimate the midpoint between Points C and F:<\/p>\n<div class=\"examplesentence\">\n\\(M=(\\frac{x_1+x_2}{2},\\frac{y_1+y_2}{2})\\)&nbsp;<br \/>\n\\(M\u2248(\\frac{0.2+(-0.4)}{2},\\frac{-350+300}{2})\\)&nbsp;<br \/>\n\\(M\u2248(\\frac{-0.2}{2},\\frac{-50}{2})\\)&nbsp;<br \/>\n\\(M\u2248(-0.1,-25)\\)\n<\/div>\n<p>\n&nbsp;<br \/>\nTo graph, we\u2019ll need to estimate the location of -25.<\/p>\n<p>I hope that this video helped you understand how to perform calculations using the points on a coordinate plane! Thanks for watching, and happy studying!<\/p>\n<\/div>\n<div class=\"spoiler\" id=\"PQs-spoiler\">\n<h2 style=\"text-align:center\"><span id=\"Graph_Practice_Questions\" class=\"m-toc-anchor\"><\/span>Graph Practice Questions<\/h2>\n\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #1:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nWhat is the distance between the points \\((2,7)\\) and \\((31,25)\\)?<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-1-1\">22.54<\/div><div class=\"PQ correct_answer\"  id=\"PQ-1-2\">34.13<\/div><div class=\"PQ\"  id=\"PQ-1-3\">27.92<\/div><div class=\"PQ\"  id=\"PQ-1-4\">31.79<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-1\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-1\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-1-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>The distance formula is:<\/p>\n<p style=\"text-align:center;\">\\(D=\\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\)<\/p>\n<p>Plugging in these points results in:<\/p>\n<p style=\"text-align: center; line-height: 50px\">\n\\(D=\\sqrt{(31-2)^2+(25-7)^2}\\)<br \/>\n\\(=\\sqrt{(29)^2+(18)^2}\\)<br \/>\n\\(=\\sqrt{841+324}\\)<br \/>\n\\(=\\sqrt{1,165} \\approx 34.13\\)<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-1-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-1-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #2:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nWhat is the midpoint of the points \\((3,5)\\) and \\((4,17)\\)?<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ correct_answer\"  id=\"PQ-2-1\">\\((\\frac{7}{2},11)\\)<\/div><div class=\"PQ\"  id=\"PQ-2-2\">\\((7,22)\\)<\/div><div class=\"PQ\"  id=\"PQ-2-3\">\\((\\frac{5}{2},6)\\)<\/div><div class=\"PQ\"  id=\"PQ-2-4\">\\((5,12)\\)<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-2\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-2\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-2-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>The formula for finding midpoint is:<\/p>\n<p style=\"text-align:center;\">\\(M=(\\frac{x_1+x_2}{2},\\frac{y_1+y_2}{2})\\)<\/p>\n<p>Plugging in these two points results in:<\/p>\n<p style=\"text-align:center; line-height: 50px\">\\((\\frac{3+4}{2},\\frac{5+17}{2})\\)\\(\\:=(\\frac{7}{2},\\frac{22}{2})=(\\frac{7}{2},11)\\)<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-2-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-2-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #3:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nWhat is the distance between the points \\((4,7)\\) and \\((7,4)\\)?<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-3-1\">6.81<\/div><div class=\"PQ\"  id=\"PQ-3-2\">2.76<\/div><div class=\"PQ\"  id=\"PQ-3-3\">7.13<\/div><div class=\"PQ correct_answer\"  id=\"PQ-3-4\">4.24<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-3\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-3\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-3-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>The distance formula is:<\/p>\n<p style=\"text-align:center;\">\\(D=\\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\)<\/p>\n<p>Plugging in these points results in:<\/p>\n<p style=\"text-align: center; line-height: 50px\">\n\\(D=\\sqrt{(7-4)^2+(4-7)^2}\\)<br \/>\n\\(=\\sqrt{(3)^2+(-3)^2}\\)<br \/>\n\\(=\\sqrt{9+9}\\)<br \/>\n\\(=\\sqrt{18}\\approx 4.24\\)<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-3-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-3-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #4:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nWhat is the midpoint of the points \\((-7,3)\\) and \\((14,-9)\\)?<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-4-1\">\\((-11,8)\\)<\/div><div class=\"PQ\"  id=\"PQ-4-2\">\\((7,-6)\\)<\/div><div class=\"PQ\"  id=\"PQ-4-3\">\\((-\\frac{11}{2},4)\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-4-4\">\\((\\frac{7}{2},-3)\\)<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-4\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-4\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-4-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>The formula for finding midpoint is:<\/p>\n<p style=\"text-align:center;\">\\(M=(\\frac{x_1+x_2}{2},\\frac{y_1+y_2}{2})\\)<\/p>\n<p>Plugging in these two points results in:<\/p>\n<p style=\"text-align:center; line-height: 50px\">\\((\\frac{-7+14}{2},\\frac{3+(-9)}{2})\\)\\(\\:=(\\frac{7}{2},\\frac{-6}{2})\\)\\(=(\\frac{7}{2},-3)\\)<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-4-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-4-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #5:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nWhat is the distance between the points \\((-12,4)\\) and \\((6,-9)\\)?<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ correct_answer\"  id=\"PQ-5-1\">22.20<\/div><div class=\"PQ\"  id=\"PQ-5-2\">14.19<\/div><div class=\"PQ\"  id=\"PQ-5-3\">27.63<\/div><div class=\"PQ\"  id=\"PQ-5-4\">19.41<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-5\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-5\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-5-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>The distance formula is:<\/p>\n<p style=\"text-align:center;\">\\(D=\\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\)<\/p>\n<p>Plugging in these points results in:<\/p>\n<p style=\"text-align: center; line-height: 50px\">\n\\(D=\\sqrt{(6-(-12))^2+(-9-4)^2}\\)<br \/>\n\\(=\\sqrt{(18)^2+(-13)^2}\\)<br \/>\n\\(=\\sqrt{324+169}\\)<br \/>\n\\(=\\sqrt{493}\\approx 22.20\\)<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-5-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-5-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #6:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>What is the distance between the points \\((-3,7)\\) and \\((16,11)\\)?<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-6-1\">318.73<\/div><div class=\"PQ correct_answer\"  id=\"PQ-6-2\">19.42<\/div><div class=\"PQ\"  id=\"PQ-6-3\">21<\/div><div class=\"PQ\"  id=\"PQ-6-4\">377<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-6\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-6\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-6-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>The formula for distance between two points, \\((x_1, y_1)\\) and \\((x_2, y_2)\\), is:<\/p>\n<p style=\"text-align:center;\">\\(D=\\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\)<\/p>\n<p>Plug in the given points and solve.<\/p>\n<p style=\"text-align:center; line-height: 50px\">\\(D=\\sqrt{(16-(-3))^2+(11-7)^2}\\)\\(\\:=\\sqrt{(19)^2+(4)^2}=\\sqrt{361+16}\\)\\(\\:=\\sqrt{377}\\approx 19.42\\)<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-6-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-6-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #7:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>What is the distance between the points \\((14,-9)\\) and \\((12,11)\\)?<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ correct_answer\"  id=\"PQ-7-1\">20.1<\/div><div class=\"PQ\"  id=\"PQ-7-2\">404<\/div><div class=\"PQ\"  id=\"PQ-7-3\">13<\/div><div class=\"PQ\"  id=\"PQ-7-4\">412.7<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-7\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-7\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-7-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>The formula for distance between two points, \\((x_1, y_1)\\) and \\((x_2, y_2)\\), is:<\/p>\n<p style=\"text-align:center;\">\\(D=\\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\)<\/p>\n<p>Plug in the given points and solve.<\/p>\n<p style=\"text-align:center; line-height: 50px\">\\(D=\\sqrt{(12-14)^2+(11-(-9))^2}\\)\\(\\:=\\sqrt{(-2)^2+(20)^2}=\\sqrt{4+400}\\)\\(\\:=\\sqrt{404}\u224820.1\\)<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-7-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-7-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #8:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>What is the distance between the points \\((-7,-1)\\) and \\((8,-2)\\)?<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-8-1\">226<\/div><div class=\"PQ\"  id=\"PQ-8-2\">211.72<\/div><div class=\"PQ\"  id=\"PQ-8-3\">19<\/div><div class=\"PQ correct_answer\"  id=\"PQ-8-4\">15.03<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-8\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-8\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-8-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>The formula for distance between two points, \\((x_1, y_1)\\) and \\((x_2, y_2)\\), is:<\/p>\n<p style=\"text-align:center;\">\\(D=\\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\)<\/p>\n<p>Plug in the given points and solve.<\/p>\n<p style=\"text-align:center; line-height: 50px\">\\(D=\\sqrt{(8-(-7))^2+(-2-(-1))^2}\\)\\(=\\sqrt{(15)^2+(-1)^2}\\)\\(\\:=\\sqrt{225+1}\\)<\/span>\\(\\:=\\sqrt{226}\u224815.03\\)<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-8-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-8-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #9:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>What is the distance between the points \\((21,-7)\\) and \\((-13,12)\\)?<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ correct_answer\"  id=\"PQ-9-1\">38.95<\/div><div class=\"PQ\"  id=\"PQ-9-2\">1,493.86<\/div><div class=\"PQ\"  id=\"PQ-9-3\">42<\/div><div class=\"PQ\"  id=\"PQ-9-4\">1,517<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-9\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-9\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-9-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>The formula for distance between two points, \\((x_1, y_1)\\) and \\((x_2, y_2)\\), is:<\/p>\n<p style=\"text-align:center;\">\\(D=\\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\)<\/p>\n<p>Plug in the given points and solve.<\/p>\n<p style=\"text-align:center; line-height: 50px\">\\(D=\\sqrt{(-13-21)^2+(12-(-7))^2}\\)\\(\\:=\\sqrt{(-34)^2+(19)^2}\\)\\(\\:=\\sqrt{1{,}156+361}\\)\\(\\:=\\sqrt{1{,}517} \\approx 38.95\\)<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-9-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-9-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #10:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>What is the distance between the points \\((16,17)\\) and \\((-14,2)\\)?<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-10-1\">1,125<\/div><div class=\"PQ\"  id=\"PQ-10-2\">1,197.63<\/div><div class=\"PQ\"  id=\"PQ-10-3\">33.54<\/div><div class=\"PQ\"  id=\"PQ-10-4\">36<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-10\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-10\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-10-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>The formula for distance between two points, \\((x_1, y_1)\\) and \\((x_2, y_2)\\), is:<\/p>\n<p style=\"text-align:center;\">\\(D=\\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\)<\/p>\n<p>Plug in the given points and solve.<\/p>\n<p style=\"text-align:center; line-height: 50px\">\\(D=\\sqrt{(-14-16)^2+(2-17)^2}\\)\\(\\:=\\sqrt{(-30)^2+(-15)^2}\\)\\(\\:=\\sqrt{900+225}\\)\\(\\:=\\sqrt{1{,}125}\u224833.54\\)<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-10-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-10-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div><\/div>\n<\/div>\n\n<div class=\"home-buttons\">\n<p><a href=\"https:\/\/www.mometrix.com\/academy\/algebra-ii\/\">Return to Algebra II Videos<\/a><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Return to Algebra II Videos<\/p>\n","protected":false},"author":1,"featured_media":91741,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":{"0":"post-58244","1":"page","2":"type-page","3":"status-publish","4":"has-post-thumbnail","6":"page_category-functions-and-their-graphs-videos","7":"page_category-math-advertising-group","8":"page_type-video","9":"content_type-practice-questions","10":"subject_matter-math"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/58244","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/comments?post=58244"}],"version-history":[{"count":6,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/58244\/revisions"}],"predecessor-version":[{"id":280694,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/58244\/revisions\/280694"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media\/91741"}],"wp:attachment":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media?parent=58244"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}