{"id":259,"date":"2017-08-23T04:33:47","date_gmt":"2017-08-23T04:33:47","guid":{"rendered":"http:\/\/americanboard.org\/Subjects\/elementary-education\/?page_id=259"},"modified":"2017-09-25T20:56:06","modified_gmt":"2017-09-25T20:56:06","slug":"transformations","status":"publish","type":"page","link":"https:\/\/americanboard.org\/Subjects\/elementary-education\/transformations\/","title":{"rendered":"Transformations"},"content":{"rendered":"<div class=\"twelve columns\" style=\"margin-top: 10%;\">\n<div class=\"advance\"><a class=\"button button-primary\" href=\"http:\/\/americanboard.org\/Subjects\/elementary-education\/properties-of-polygons\">\u2b05 Previous Lesson<\/a>\u00a0<a class=\"button\" href=\"http:\/\/americanboard.org\/Subjects\/elementary-education\/geometry-measurement\">Workshop Index<\/a>\u00a0<a class=\"button button-primary\" href=\"http:\/\/americanboard.org\/Subjects\/elementary-education\/three-dimensional-figures-or-solids\">Next Lesson \u27a1<\/a><\/div>\n<p><!-- CONTENT BEGINS HERE --><\/p>\n<h1 id=\"title\">Transformations<\/h1>\n<h4>Objective<\/h4>\n<p>In this lesson, we&#8217;ll explore transformations, which are changes to the size, shape, location, or orientation of a figure.<\/p>\n<h4>Previously Covered<\/h4>\n<ul>\n<li>In the previous lesson we reviewed a few properties of polygons.<\/li>\n<\/ul>\n<section>\n<h3>Transformations<\/h3>\n<p>Let&#8217;s investigate three types of transformations: translations, reflections, and rotations.<\/p>\n<h4>Translation<\/h4>\n<p>A figure undergoes a <em>translation<\/em> when it slides a certain distance in a certain direction. The translated figure is called the <em>image<\/em> of the original figure. It is congruent to the original figure.<\/p>\n<p><center><img decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/elementary-education\/wp-content\/uploads\/sites\/4\/2017\/08\/translation5.gif\" alt=\"Translation\" \/><\/center><\/p>\n<p class=\"figcaption\">The yellow figure (M) has been translated a distance of 9.00 cm to the right. The orange figure (J) is the translated image of the yellow figure (M).<\/p>\n<h4>Reflection<\/h4>\n<p>A <em>reflection<\/em> is a transformation that produces a mirror image of the original figure by flipping it across a line. While the reflection changes the object\u2019s orientation (top and bottom, left and right), the reflected image is congruent to the original figure.<\/p>\n<p><center><img decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/elementary-education\/wp-content\/uploads\/sites\/4\/2017\/08\/reflection7.gif\" alt=\"Reflection\" \/><\/center><\/p>\n<p class=\"figcaption\">The yellow figure (left) has been reflected over the dotted line to produce the orange mirror image (right).<\/p>\n<p>The image below shows a figure that has a property called <strong>bilateral symmetry<\/strong>. The figure can be divided in half by a line of symmetry so that one side is a mirror image of the other side. In fact, this figure has many lines of symmetry, but only one is drawn here. All regular polygons have bilateral symmetry.<\/p>\n<p><center><img decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/elementary-education\/wp-content\/uploads\/sites\/4\/2017\/08\/bilateral-symmetry8.gif\" alt=\"Bilateral symmetry\" \/><\/center><\/p>\n<p class=\"figcaption\">Bilateral Symmetry<\/p>\n<h4>Rotation<\/h4>\n<p>A rotation is a transformation that rotates an object around a point. While the rotation changes the object\u2019s orientation, the rotated image is congruent to the original figure.<\/p>\n<p><center><img decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/elementary-education\/wp-content\/uploads\/sites\/4\/2017\/08\/rotation8.gif\" alt=\"Rotation\" \/><\/center><\/p>\n<p class=\"figcaption\">The yellow figure has been rotated 215\u00b0 around point A to produce the orange figure.<\/p>\n<p>The equilateral triangle below has a property called <strong>rotational symmetry<\/strong>. A figure has this property if it can be rotated around a point by less than 360\u00b0 and the object appears unchanged. This figure can be rotated 120\u00b0 or 240\u00b0 and it will appear unchanged.<\/p>\n<p><center><img decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/elementary-education\/wp-content\/uploads\/sites\/4\/2017\/08\/rotational-symmetryz.gif\" alt=\"Rotational Symmetry\" \/><\/center><\/p>\n<p class=\"figcaption\">Polygon with Rotational Symmetry<\/p>\n<section class=\"question\">\n<h4>Question<\/h4>\n<p>Which of these is an example of a translation?<\/p>\n<ol>\n<li><img decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/elementary-education\/wp-content\/uploads\/sites\/4\/2017\/08\/translationquestionanswerAz.gif\" alt=\"Answer A\" \/><\/li>\n<li><img decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/elementary-education\/wp-content\/uploads\/sites\/4\/2017\/08\/translationquestionanswerBz.gif\" alt=\"Answer B\" \/><\/li>\n<li><img decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/elementary-education\/wp-content\/uploads\/sites\/4\/2017\/08\/translationquestionanswerCz.gif\" alt=\"Answer C\" \/><\/li>\n<li><img decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/elementary-education\/wp-content\/uploads\/sites\/4\/2017\/08\/translationquestionanswerDz.gif\" alt=\"Answer D\" \/><\/li>\n<\/ol>\n<p><a class=\"q-answer button button-primary\">Reveal Answer<\/a><\/p>\n<p class=\"q-reveal\">The correct answer is B. A translation is a transformation that slides a figure a certain distance in a certain direction. Choice A shows rotation, which rotates a figure around a given point. Choice C shows a reflection, which produces a mirror image of a figure over a line. Choice D doesn&#8217;t show anything.<\/p>\n<\/section>\n<h3>Review<\/h3>\n<ul>\n<li>Transformations are changes to the size, shape, location, or orientation of a figure.<\/li>\n<li>Translation occurs when a figure is moved a certain distance in a certain direction.<\/li>\n<li>Reflection produces a mirror image of the original figure.<\/li>\n<li>Rotation moves an object around a point.<\/li>\n<\/ul>\n<\/section>\n<p><!-- CONTENT ENDS HERE --><\/p>\n<div class=\"advance\"><a class=\"button button-primary\" href=\"http:\/\/americanboard.org\/Subjects\/elementary-education\/properties-of-polygons\">\u2b05 Previous Lesson<\/a>\u00a0<a class=\"button\" href=\"http:\/\/americanboard.org\/Subjects\/elementary-education\/geometry-measurement\">Workshop Index<\/a>\u00a0<a class=\"button button-primary\" href=\"http:\/\/americanboard.org\/Subjects\/elementary-education\/three-dimensional-figures-or-solids\">Next Lesson \u27a1<\/a><\/div>\n<p><a class=\"backtotop\" href=\"#title\">Back to Top<\/a><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u2b05 Previous Lesson\u00a0Workshop Index\u00a0Next Lesson \u27a1 Transformations Objective In this lesson, we&#8217;ll explore transformations, which are changes to the size, shape, location, or orientation of a figure. Previously Covered In the previous lesson we reviewed a few properties of polygons. Transformations Let&#8217;s investigate three types of transformations: translations, reflections, and rotations. Translation A figure undergoes [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-259","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/americanboard.org\/Subjects\/elementary-education\/wp-json\/wp\/v2\/pages\/259","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/americanboard.org\/Subjects\/elementary-education\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/americanboard.org\/Subjects\/elementary-education\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/americanboard.org\/Subjects\/elementary-education\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/americanboard.org\/Subjects\/elementary-education\/wp-json\/wp\/v2\/comments?post=259"}],"version-history":[{"count":6,"href":"https:\/\/americanboard.org\/Subjects\/elementary-education\/wp-json\/wp\/v2\/pages\/259\/revisions"}],"predecessor-version":[{"id":1390,"href":"https:\/\/americanboard.org\/Subjects\/elementary-education\/wp-json\/wp\/v2\/pages\/259\/revisions\/1390"}],"wp:attachment":[{"href":"https:\/\/americanboard.org\/Subjects\/elementary-education\/wp-json\/wp\/v2\/media?parent=259"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}