{"id":4122,"date":"2013-06-27T17:52:02","date_gmt":"2013-06-27T17:52:02","guid":{"rendered":"http:\/\/www.mometrix.com\/academy\/?page_id=4122"},"modified":"2026-03-28T10:45:28","modified_gmt":"2026-03-28T15:45:28","slug":"reflection","status":"publish","type":"page","link":"https:\/\/www.mometrix.com\/academy\/reflection\/","title":{"rendered":"Reflecting Points on a Coordinate Plane"},"content":{"rendered":"\n\t\t\t<div id=\"mmDeferVideoEncompass_Wv_ML-cD8sE\" 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_Wv_ML-cD8sE\" data-source-videoID=\"Wv_ML-cD8sE\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" alt=\"Reflecting Points on a Coordinate Plane Video\" height=\"464\" width=\"825\" class=\"size-full\" data-matomo-title = \"Reflecting Points on a Coordinate Plane\">\n\t\t\t<\/picture>\n\t\t\t<\/div>\n\t\t\t<style>img#videoThumbnailImage_Wv_ML-cD8sE:hover {cursor:pointer;} img#videoThumbnailImage_Wv_ML-cD8sE {background-size:contain;background-image:url(\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/745-reflection-in-a-plane-1-1.webp\");}<\/style>\n\t\t\t<script defer>\n\t\t\t  jQuery(\"img#videoThumbnailImage_Wv_ML-cD8sE\").click(function() {\n\t\t\t\tlet videoId = jQuery(this).attr(\"data-source-videoID\");\n\t\t\t\tlet helpTag = '<div id=\"mmDeferVideoYTMessage_Wv_ML-cD8sE\" 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\",\"Reflecting Points on a Coordinate Plane\");\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_Wv_ML-cD8sE\").html(tag);\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_Wv_ML-cD8sE\").prepend(helpTag);\n\t\t\t\tsetTimeout(function(){jQuery(\"div#mmDeferVideoYTMessage_Wv_ML-cD8sE\").css(\"display\", \"block\");}, 2000);\n\t\t\t  });\n\t\t\t  \n\t\t\t<\/script>\n\t\t\n<p><script>\nfunction gkH_Function() {\n  var x = document.getElementById(\"gkH\");\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=\"gkH_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=\"gkH\" style=\"display:none;\">\n<ul>\n<li class=\"toc-h2\"><a href=\"#Reflections_Over_a_Line\" class=\"smooth-scroll\">Reflections Over a Line<\/a>\n<ul><\/li>\n<li class=\"toc-h3\"><a href=\"#Example_1\" class=\"smooth-scroll\">Example #1<\/a><\/li>\n<li class=\"toc-h3\"><a href=\"#Example_2\" class=\"smooth-scroll\">Example #2<\/a><\/li>\n<li class=\"toc-h3\"><a href=\"#Common_Ways_to_Reflect_Figures\" class=\"smooth-scroll\">Common Ways to Reflect Figures<\/a><\/li>\n<\/ul>\n<\/li>\n<li class=\"toc-h2\"><a href=\"#Reflections_Over_a_Point\" class=\"smooth-scroll\">Reflections Over a Point<\/a>\n<ul><\/li>\n<li class=\"toc-h3\"><a href=\"#Example_1_1\" class=\"smooth-scroll\">Example #1<\/a><\/li>\n<li class=\"toc-h3\"><a href=\"#Example_2_1\" class=\"smooth-scroll\">Example #2<\/a><\/li>\n<li class=\"toc-h3\"><a href=\"#Example_3\" class=\"smooth-scroll\">Example #3<\/a><\/li>\n<\/ul>\n<\/li>\n<li class=\"toc-h2\"><a href=\"#Reflecting_Points_on_a_Coordinate_Plane_Practice_Questions\" class=\"smooth-scroll\">Reflecting Points on a Coordinate Plane 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>Hi, and welcome to this video about reflection! In this video, we will explore reflection of a figure over a line and reflection of a figure on a point. Let\u2019s get started!<\/p>\n<p>When we think of the term <strong>reflection<\/strong>, we most likely think of looking in a mirror or a still body of water. This idea is related to what happens when we reflect figures on the <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/cartesian-coordinate-plane-and-graphing\/\">coordinate plane<\/a>. Like I mentioned, there are two main types of reflections: reflections over a line and reflections on a point.<\/p>\n<h2><span id=\"Reflections_Over_a_Line\" class=\"m-toc-anchor\"><\/span>Reflections Over a Line<\/h2>\n<p>\nLet\u2019s start by looking at reflections over a line.<\/p>\n<p>We can reflect a figure in the coordinate plane over any line in the <strong>coordinate plane<\/strong>.<\/p>\n<h3><span id=\"Example_1\" class=\"m-toc-anchor\"><\/span>Example #1<\/h3>\n<p>\nHere\u2019s a triangle reflected over the line \\(x=7\\).<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/09\/Reflection-01.svg\" alt=\"\" width=\"\" height=\"\" class=\"aligncenter size-full wp-image-215971\" role=\"img\" style=\"box-shadow: 1.5px 1.5px 3px gray;\" \/><\/p>\n<p>The triangle on the left is our original figure, or pre-image, named Triangle ABC. The triangle on the right is our reflected figure, or image, named Triangle A\u2019B\u2019C\u2019. <strong>Prime notation<\/strong> designates the figure that is the image. Point A on the preimage corresponds to point A\u2019 on the image, and so forth.<\/p>\n<p>Now there are a few things to notice here:<\/p>\n<p>Firstly, the preimage and image are congruent, but \u201cflipped\u201d.<\/p>\n<p>You\u2019ll also notice that all corresponding points on the preimage and image are the same distance from the line of reflection but in the opposite direction.<\/p>\n<p>And lastly, the <strong>line of reflection<\/strong> bisects all segments connecting corresponding points of the preimage and image.<\/p>\n<h3><span id=\"Example_2\" class=\"m-toc-anchor\"><\/span>Example #2<\/h3>\n<p>\nNow, here is a <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/area-and-perimeter-of-a-trapezoid\/\">trapezoid<\/a> being reflected over three different lines. <\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/09\/Reflection-in-a-Plane-example-1-scaled.webp\" alt=\"\" width=\"\" height=\"\" class=\"aligncenter size-full wp-image-215971\" role=\"img\" style=\"box-shadow: 1.5px 1.5px 3px gray;\" \/><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/09\/Reflection-in-a-Plane-example-2-scaled.webp\" alt=\"\" width=\"\" height=\"\" class=\"aligncenter size-full wp-image-215971\" role=\"img\" style=\"box-shadow: 1.5px 1.5px 3px gray;\" \/><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/09\/Reflection-in-a-Plane-example-3-scaled.webp\" alt=\"\" width=\"\" height=\"\" class=\"aligncenter size-full wp-image-215971\" role=\"img\" style=\"box-shadow: 1.5px 1.5px 3px gray;\" \/><\/p>\n<p>Notice how the three properties we just discussed hold true, but also notice how, to actually create a reflection, it often involves simply counting the distances between the line of reflection and the points, or adding and subtracting coordinates.<\/p>\n<p>In some cases, the line of reflection may be on the edge\u2014or even inside\u2014the figure.<\/p>\n<h3><span id=\"Common_Ways_to_Reflect_Figures\" class=\"m-toc-anchor\"><\/span>Common Ways to Reflect Figures<\/h3>\n<p>\nThree common ways to reflect figures are over the \\(x\\)-axis, \\(y\\)-axis, and the line \\(y=x\\).<\/p>\n<p>Something to notice as we look at these is that the signs of the coordinates change. <\/p>\n<p>For example, when a figure is reflected over the \\(x\\)-axis, notice the \\(y\\)-coordinates change sign.<\/p>\n<p>When a figure is reflected over the \\(y\\)-axis, notice the \\(x\\)-coordinates change sign.<\/p>\n<p>When a figure is reflected over the line \\(y=x\\), notice that the coordinates change order.<\/p>\n<h2><span id=\"Reflections_Over_a_Point\" class=\"m-toc-anchor\"><\/span>Reflections Over a Point<\/h2>\n<p>\nWe can also reflect a figure in the coordinate plane in any point on the coordinate plane.<\/p>\n<h3><span id=\"Example_1\" class=\"m-toc-anchor\"><\/span>Example #1<\/h3>\n<p>\nHere\u2019s a dart reflected in the point (12,10).<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/09\/dart-reflection-04.svg\" alt=\"\" width=\"\" height=\"\" class=\"aligncenter size-full wp-image-215971\" role=\"img\" style=\"box-shadow: 1.5px 1.5px 3px gray;\" \/><\/p>\n<p>The point the dart is reflected over is called, you guessed it, the <strong>point of reflection<\/strong>.<\/p>\n<p>The properties of reflections in points are very similar to those of reflections over lines. The preimage and image are congruent, but the image is a 180-degree rotation of the preimage. All corresponding points on the preimage and image are the same, but opposite, distance from the point of reflection.<\/p>\n<p>And, the point of reflection is the midpoint of all segments connecting corresponding points of the preimage and image.<\/p>\n<p>Sounds just like reflection over a line, right?<\/p>\n<h3><span id=\"Example_2\" class=\"m-toc-anchor\"><\/span>Example #2<\/h3>\n<p>\nHere is a kite being reflected over several different points. <\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/09\/kite1-scaled.webp\" alt=\"\" width=\"\" height=\"\" class=\"aligncenter size-full wp-image-215971\" role=\"img\" style=\"box-shadow: 1.5px 1.5px 3px gray;\" \/><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/09\/kite2-scaled.webp\" alt=\"\" width=\"\" height=\"\" class=\"aligncenter size-full wp-image-215971\" role=\"img\" style=\"box-shadow: 1.5px 1.5px 3px gray;\" \/><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/09\/kite3-scaled.webp\" alt=\"\" width=\"\" height=\"\" class=\"aligncenter size-full wp-image-215971\" role=\"img\" style=\"box-shadow: 1.5px 1.5px 3px gray;\" \/><\/p>\n<p>The point of reflection can be on the edge\u2014or even inside\u2014the figure. Notice how our properties still hold true.<\/p>\n<h3><span id=\"Example_3\" class=\"m-toc-anchor\"><\/span>Example #3<\/h3>\n<p>\nAnd finally, let\u2019s look at one last reflection. One often-used reflection is one about the origin (0,0). When a figure is reflected about the origin, the signs of all coordinates change.<\/p>\n<p>That\u2019s all for this video. Thanks for watching, and happy studying!<\/p>\n<\/div>\n<div class=\"spoiler\" id=\"PQs-spoiler\">\n<h2 style=\"text-align:center\"><span id=\"Reflecting_Points_on_a_Coordinate_Plane_Practice_Questions\" class=\"m-toc-anchor\"><\/span>Reflecting Points on a Coordinate Plane 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 \/>\nThe coordinates for \\(\\triangle ABC\\) are listed below. This triangle is reflected across the \\(x\\)-axis to create \\(\\triangle A\u2019B\u2019C\u2019\\). What are the coordinates of \\(\\triangle A\u2019B\u2019C&#8217;\\)?<\/p>\n<ul style=\"list-style-type: none; margin-left: 1.2em\">\n<li style=\"margin-bottom: 8px\">\\(A(0,7)\\)<\/li>\n<li style=\"margin-bottom: 8px\">\\(B(3,-5)\\)<\/li>\n<li>\\(C(-3,5)\\)<\/li>\n<\/ul>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-1-1\"><p style=\"line-height: 30px; margin-bottom: 0em\">\\(A\u2019(0,-7)\\)<br>\r\n\\(B\u2019(-3,5)\\)<br>\r\n\\(C\u2019(3,-5)\\)<\/p><\/div><div class=\"PQ correct_answer\"  id=\"PQ-1-2\"><p style=\"line-height: 30px; margin-bottom: 0em\">\\(A\u2019(0,-7)\\)<br>\r\n\\(B\u2019(3,5)\\)<br>\r\n\\(C\u2019(-3,-5)\\)<\/p><\/div><div class=\"PQ\"  id=\"PQ-1-3\"><p style=\"line-height: 30px; margin-bottom: 0em\">\\(A\u2019(0,7)\\)<br>\r\n\\(B\u2019(-3,-5)\\)<br>\r\n\\(C\u2019(3,5)\\)<\/p><\/div><div class=\"PQ\"  id=\"PQ-1-4\"><p style=\"line-height: 30px; margin-bottom: 0em\">\\(A\u2019(7,0)\\)<br>\r\n\\(B\u2019(-5,3)\\)<br>\r\n\\(C\u2019(5,-3)\\)<\/p><\/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 rule for reflecting across the \\(x\\)-axis is \\((x,y)\\rightarrow (x,-y)\\). When we apply this rule to the points of the vertices of \\(\\triangle ABC\\), we get:<\/p>\n<ul style=\"list-style-type: none; margin-left: 1.2em\">\n<li style=\"margin-bottom: 8px\">\\(A(0,7)\\)<\/li>\n<li style=\"margin-bottom: 8px\">\\(B(3,-5)\\)<\/li>\n<li>\\(C(-3,5)\\)<\/li>\n<\/ul>\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 \/>\nThe coordinates for trapezoid \\(PQRS\\) are listed below. This trapezoid is reflected across the line \\(y=x\\) to create trapezoid \\(P\u2019Q\u2019R\u2019S\u2019\\). What are the coordinates of trapezoid \\(P\u2019Q\u2019R\u2019S\u2019\\)? <\/p>\n<ul style=\"list-style-type: none; margin-left: 1.2em\">\n<li style=\"margin-bottom: 8px\">\\(P(2,3)\\)<\/li>\n<li style=\"margin-bottom: 8px\">\\(Q(6,3)\\)<\/li>\n<li style=\"margin-bottom: 8px\">\\(R(8,1)\\)<\/li>\n<li>\\(S(0,1)\\)<\/li>\n<\/ul>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ correct_answer\"  id=\"PQ-2-1\"><p style=\"line-height: 30px; margin-bottom: 0em\">\\(P'(3,2)\\)<br>\r\n\\(Q'(3,6)\\)<br>\r\n\\(R'(1,8)\\)<br>\r\n\\(S'(1,0)\\)<\/p><\/div><div class=\"PQ\"  id=\"PQ-2-2\"><p style=\"line-height: 30px; margin-bottom: 0em\">\\(P'(-3,-2)\\)<br>\r\n\\(Q'(-3,-6)\\)<br>\r\n\\(R'(-1,-8)\\)<br>\r\n\\(S'(-1,0)\\)<\/p><\/div><div class=\"PQ\"  id=\"PQ-2-3\"><p style=\"line-height: 30px; margin-bottom: 0em\">\\(P'(2,-3)\\)<br>\r\n\\(Q'(6,-3)\\)<br>\r\n\\(R'(8,-1)\\)<br>\r\n\\(S'(0,-1)\\)<\/p><\/div><div class=\"PQ\"  id=\"PQ-2-4\"><p style=\"line-height: 30px; margin-bottom: 0em\">\\(P'(-2,3)\\)<br>\r\n\\(Q'(-6,3)\\)<br>\r\n\\(R'(-8,1)\\)<br>\r\n\\(S'(0,1)\\)<\/p><\/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 rule for reflecting across the line \\(y=x\\) is \\((x,y)\\rightarrow(y,x)\\). When we apply the rule to the points of the vertices of trapezoid \\(PQRS\\), we get:<\/p>\n<ul style=\"list-style-type: none; margin-left: 1.2em\">\n<li style=\"margin-bottom: 8px\">\\(P'(3,2)\\)<\/li>\n<li style=\"margin-bottom: 8px\">\\(Q'(3,6)\\)<\/li>\n<li style=\"margin-bottom: 8px\">\\(R'(1,8)\\)<\/li>\n<li>\\(S'(1,0)\\)<\/li>\n<\/ul>\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 \/>\nRectangle \\(LMNO\\) has been reflected across a certain line to create rectangle \\(L\u2019M\u2019N\u2019O\u2019\\).<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Reflection-PQ-1.png\" alt=\"coordinate grid with two rectangles, rectangle LMNO and rotated rectangle L&#039;M&#039;N&#039;O&#039;\" width=\"356.5\" height=\"517.5\" class=\"aligncenter size-full wp-image-106269\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Reflection-PQ-1.png 1030w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Reflection-PQ-1-264x300.png 264w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Reflection-PQ-1-901x1024.png 901w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Reflection-PQ-1-768x872.png 768w\" sizes=\"(max-width: 1030px) 100vw, 1030px\" \/><\/p>\n<p>Which line was rectangle \\(LMNO\\) reflected across? <\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-3-1\">\\(y\\)-axis<\/div><div class=\"PQ\"  id=\"PQ-3-2\">\\(x\\)-axis<\/div><div class=\"PQ\"  id=\"PQ-3-3\">\\(y=x\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-3-4\">\\(y=-x\\)<\/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>Start by looking at the coordinates of the vertices of rectangle \\(LMNO\\) and \\(L\u2019M\u2019N\u2019O\u2019\\) next to each other.<\/p>\n<ul style=\"list-style-type: none; margin-left: 1.2em\">\n<li style=\"margin-bottom: 8px;\">\\(L(-6,8)\\to L\u2019(-8,6)\\)<\/li>\n<li style=\"margin-bottom: 8px;\">\\(M(4,8)\\to M\u2019(-8,-4)\\)<\/li>\n<li style=\"margin-bottom: 8px;\">\\(N(4,4)\\to N\u2019(-4,-4)\\)<\/li>\n<li>\\(O(-6,4)\\to O\u2019(-4,6)\\)<\/li>\n<\/ul>\n<p> When examined closely, we see that the rule that was applied here is \\((x,y)\\to (-y,-x)\\), which is the rule for reflecting across the line \\(y=-x\\). It can also be thought of as reflecting across the line \\(y=x\\) and also reflecting about the origin, which is why the rule is \\((x,y)\\to (-y,-x)\\).<\/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 \/>\nQuadrilateral \\(ABCD\\) is shown on the coordinate grid. When quadrilateral \\(ABCD\\) is reflected across the origin, quadrilateral \\(A\u2019B\u2019C\u2019D\u2019\\) is created.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/12\/Reflection-PQ-2.png\" alt=\"diamond ABCD in the third quadrant\" width=\"329\" height=\"495\" class=\"aligncenter size-full wp-image-106272\" \/><\/p>\n<p>What are the coordinates of the vertices of quadrilateral \\(A\u2019B\u2019C\u2019D\u2019\\)?<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-4-1\"><p style=\"line-height: 30px; margin-bottom: 0em\">\\(A'(-7,4)\\)<br>\r\n\\(B'(-5,1)\\)<br>\r\n\\(C'(-3,4)\\)<br>\r\n\\(D'(-5,7)\\)<\/p><\/div><div class=\"PQ\"  id=\"PQ-4-2\"><p style=\"line-height: 30px; margin-bottom: 0em\">\\(A'(7,-4)\\)<br>\r\n\\(B'(5,-1)\\)<br>\r\n\\(C'(3,-4)\\)<br>\r\n\\(D'(5,-7)\\)<\/p><\/div><div class=\"PQ\"  id=\"PQ-4-3\"><p style=\"line-height: 30px; margin-bottom: 0em\">\\(A'(-4,-7)\\)<br>\r\n\\(B'(-1,-5)\\)<br>\r\n\\(C'(-4,-3)\\)<br>\r\n\\(D'(-7,-5)\\)<\/p><\/div><div class=\"PQ correct_answer\"  id=\"PQ-4-4\"><p style=\"line-height: 30px; margin-bottom: 0em\">\\(A'(7,4)\\)<br>\r\n\\(B'(5,1)\\)<br>\r\n\\(C'(3,4)\\)<br>\r\n\\(D'(5,7)\\)<\/p><\/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 rule for reflecting across the origin is \\((x,y)\\to (-x,-y)\\).<\/p>\n<p>Start by finding the vertices of quadrilateral \\(ABCD\\) from the coordinate plane, which are:<\/p>\n<ul style=\"list-style-type: none; margin-left: 1.2em\">\n<li style=\"margin-bottom: 8px;\">\\(A(-7,-4)\\)<\/li>\n<li style=\"margin-bottom: 8px;\">\\(B(-5,-1)\\)<\/li>\n<li style=\"margin-bottom: 8px;\">\\(C(-3,-4)\\)<\/li>\n<li>\\(D(-5,-7)\\)<\/li>\n<\/ul>\n<p>When we apply the rule, we get:<\/p>\n<ul style=\"list-style-type: none; margin-left: 1.2em\">\n<li style=\"margin-bottom: 8px;\">\\(A'(7,4)\\)<\/li>\n<li style=\"margin-bottom: 8px;\">\\(B'(5,1)\\)<\/li>\n<li style=\"margin-bottom: 8px;\">\\(C'(3,4)\\)<\/li>\n<li>\\(D'(5,7)\\)<\/li>\n<\/ul>\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 \/>\nThe coordinates for \\(\\triangle DEF\\) and \\(\\triangle D&#8217;E&#8217;F&#8217;\\) are listed below. \\(\\triangle DEF\\) is reflected across a certain line to create \\(\\triangle D\u2019E\u2019F\u2019\\) with coordinates. Which line was the triangle reflected across?<\/p>\n<ul style=\"list-style-type: none; margin-left: 1.2em\">\n<li style=\"margin-bottom: 8px;\">\\(D(-6,2)\\)<\/li>\n<li style=\"margin-bottom: 8px;\">\\(E(4,6)\\)<\/li>\n<li>\\(F(1,-2)\\)<\/li>\n<\/ul>\n<ul style=\"list-style-type: none; margin-left: 1.2em\">\n<li style=\"margin-bottom: 8px;\">\\(D'(6,2)\\)<\/li>\n<li style=\"margin-bottom: 8px;\">\\(E'(-4,6)\\)<\/li>\n<li>\\(F'(-1,-2)\\)<\/li>\n<\/ul>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ correct_answer\"  id=\"PQ-5-1\">\\(y\\)-axis<\/div><div class=\"PQ\"  id=\"PQ-5-2\">\\(x\\)-axis<\/div><div class=\"PQ\"  id=\"PQ-5-3\">\\(y=x\\)<\/div><div class=\"PQ\"  id=\"PQ-5-4\">\\(y=-x\\)<\/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>We will start by comparing the original point with its reflected point and we can see that the value of the \\(y\\)-coordinate stayed the same in all three vertices, but the value of the <span style=\"white-space:nowrap\">\\(x\\)-coordinate<\/span> has the opposite sign from the original. This is the rule we follow when we are reflecting across the \\(y\\)-axis, which is \\((x,y)\\to (-x,y)\\).<\/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><\/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":99835,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"open","template":"","meta":{"footnotes":""},"class_list":{"0":"post-4122","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_category-video-pages-for-study-course-sidebar-ad","9":"page_type-video","10":"content_type-practice-questions","11":"subject_matter-math"},"aioseo_notices":[],"aioseo_head":"\n\t\t<!-- All in One SEO Pro 4.9.9 - aioseo.com -->\n\t<meta name=\"description\" content=\"There are two main types of reflections: reflections over a line and reflections on a point. 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