{"id":21695,"date":"2016-02-17T21:48:38","date_gmt":"2016-02-17T21:48:38","guid":{"rendered":"http:\/\/www.mometrix.com\/academy\/?page_id=21695"},"modified":"2026-04-27T13:40:05","modified_gmt":"2026-04-27T18:40:05","slug":"transformations-on-graphs","status":"publish","type":"page","link":"https:\/\/www.mometrix.com\/academy\/transformations-on-graphs\/","title":{"rendered":"Examples of Transformations on a Graph"},"content":{"rendered":"\n\t\t\t<div id=\"mmDeferVideoEncompass_HgctcJrSamQ\" 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_HgctcJrSamQ\" data-source-videoID=\"HgctcJrSamQ\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" alt=\"Examples of Transformations on a Graph Video\" height=\"720\" width=\"1280\" class=\"size-full\" data-matomo-title = \"Examples of Transformations on a Graph\">\n\t\t\t<\/picture>\n\t\t\t<\/div>\n\t\t\t<style>img#videoThumbnailImage_HgctcJrSamQ:hover {cursor:pointer;} img#videoThumbnailImage_HgctcJrSamQ {background-size:contain;background-image:url(\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2026\/04\/transformations-on-a-graph-thumb.jpg\");}<\/style>\n\t\t\t<script defer>\n\t\t\t  jQuery(\"img#videoThumbnailImage_HgctcJrSamQ\").click(function() {\n\t\t\t\tlet videoId = jQuery(this).attr(\"data-source-videoID\");\n\t\t\t\tlet helpTag = '<div id=\"mmDeferVideoYTMessage_HgctcJrSamQ\" 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\",\"Examples of Transformations on a Graph\");\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_HgctcJrSamQ\").html(tag);\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_HgctcJrSamQ\").prepend(helpTag);\n\t\t\t\tsetTimeout(function(){jQuery(\"div#mmDeferVideoYTMessage_HgctcJrSamQ\").css(\"display\", \"block\");}, 2000);\n\t\t\t  });\n\t\t\t  \n\t\t\t<\/script>\n\t\t\n<div class=\"accordion\"><input id=\"transcript\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"transcript\">Transcript<\/label>\n<div class=\"spoiler\" id=\"transcript-spoiler\">\n<p>Hi, and welcome to this video lesson on rotation, translation, and reflection of objects on a plane.<\/p>\n<p>Here&#8217;s our object. I want to rotate it on this plane, which is like a graph or a background.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2026\/04\/Transformation-graph-1.svg\" alt=\"A small right triangle shaded in purple is located in the first quadrant of an x-y coordinate plane.\" width=\"514\" height=\"552\" class=\"aligncenter size-full wp-image-292499\"  role=\"img\" \/><\/p>\n<p>If you think of rotating this object like you would a tire, that might help. If I want to rotate this picture, that means just spinning it around its center, like this. An image can be rotated from 0 to 360 degrees, like a circle.<\/p>\n<p>Reflection is just like what it sounds: mirroring something. Take our image, and then decide which way we are going to reflect it. Perhaps to the left. Then, our reflection might look like this.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2026\/04\/Transformation-graph-2.svg\" alt=\"Graph showing two identical right triangles in purple, one in the second quadrant and one in the first quadrant, both with hypotenuses sloping downward toward the origin.\" width=\"514\" height=\"552\" class=\"aligncenter size-full wp-image-292502\"  role=\"img\" \/><\/p>\n<p>Usually in math, you are using a coordinate graph, so we might say the image is reflected across the \\(y\\)-axis, which is this vertical line here. Translation is not translating words into different languages, so don&#8217;t worry.<\/p>\n<p>Mathematical translation simply means to move something. To make it travel, like this.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2026\/04\/Transformation-graph-3.svg\" alt=\"Two right triangles, one gray and one blue, are shown on a coordinate plane with the blue triangle shifted rightward from the gray triangle. An arrow indicates the direction of shift.\" width=\"514\" height=\"552\" class=\"aligncenter size-full wp-image-292505\"  role=\"img\" \/><\/p>\n<p>Translating this image to the right two spaces on the \\(x\\)-axis (this is the horizontal line) simply means moving it to the right two spaces.<\/p>\n<p>All the different ways that we&#8217;ve moved or changed this object are called transformations. Now I&#8217;m going to give you a few examples and I want you to try to figure out how I transformed this specific object.<\/p>\n<p>Here&#8217;s an image. How has it been transformed?<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2026\/04\/Transformation-graph-4.svg\" alt=\"Two cats sit on a coordinate plane: a pink cat at (-2, 5) and a blue cat at (2, 5).\" width=\"514\" height=\"552\" class=\"aligncenter size-full wp-image-292508\"  role=\"img\" \/><\/p>\n<p>It&#8217;s been reflected across the \\(y\\)-axis, or this vertical line here. See?<\/p>\n<p>Here&#8217;s another. How has it been transformed?<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2026\/04\/Transformation-graph-5.svg\" alt=\"Two snails are on a coordinate grid; one pink snail at (-4, -3) and one blue snail at (2, -3).\" width=\"514\" height=\"552\" class=\"aligncenter size-full wp-image-292496\"  role=\"img\" \/><\/p>\n<p>Well, it&#8217;s been moved, or translated, to the left four spaces.<\/p>\n<p>I hope that helps! Thanks for watching this video lesson, and until next time, happy studying!<\/p>\n<\/div>\n<\/div>\n\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":1,"featured_media":292514,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":{"0":"post-21695","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":"subject_matter-math"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/21695","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=21695"}],"version-history":[{"count":4,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/21695\/revisions"}],"predecessor-version":[{"id":292511,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/21695\/revisions\/292511"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media\/292514"}],"wp:attachment":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media?parent=21695"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}