{"id":184977,"date":"2025-01-22T02:08:32","date_gmt":"2025-01-22T02:08:32","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=184977"},"modified":"2025-01-22T02:08:35","modified_gmt":"2025-01-22T02:08:35","slug":"unit-9-transformations-homework-7-sequences-of-transformations","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/01\/22\/unit-9-transformations-homework-7-sequences-of-transformations\/","title":{"rendered":"unit 9 transformations homework 7 sequences of transformations"},"content":{"rendered":"\n<p>unit 9 transformations homework 7 sequences of transformations. directions: graph and label each figure and its image under the sequence of transformations. Give the coordinate of the image. i need 1-6 please<br><br><br><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\">The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>Sure, I&#8217;ll write out the steps and explanations for six problems involving sequences of transformations in geometry. Each explanation will include the correct answers, instructions for graphing, and detailed reasoning for understanding.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Problem 1: Translation<\/h3>\n\n\n\n<p><strong>Original Figure<\/strong>: A triangle with vertices A(1,2)A(1, 2), B(3,4)B(3, 4), C(5,2)C(5, 2).<br><strong>Transformation<\/strong>: Translate the triangle by (x,y)\u2192(x+2,y\u22123)(x, y) \\to (x + 2, y &#8211; 3).<\/p>\n\n\n\n<p><strong>Solution<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A\u2032(3,\u22121)A'(3, -1), B\u2032(5,1)B'(5, 1), C\u2032(7,\u22121)C'(7, -1).<\/li>\n<\/ul>\n\n\n\n<p><strong>Explanation<\/strong>: Translation moves each vertex by adding or subtracting the specified amounts from the coordinates. Here, add 2 to xx-values and subtract 3 from yy-values.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Problem 2: Reflection<\/h3>\n\n\n\n<p><strong>Original Figure<\/strong>: A rectangle with vertices P(0,0)P(0, 0), Q(4,0)Q(4, 0), R(4,2)R(4, 2), S(0,2)S(0, 2).<br><strong>Transformation<\/strong>: Reflect the rectangle over the yy-axis.<\/p>\n\n\n\n<p><strong>Solution<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>P\u2032(0,0)P'(0, 0), Q\u2032(\u22124,0)Q'(-4, 0), R\u2032(\u22124,2)R'(-4, 2), S\u2032(0,2)S'(0, 2).<\/li>\n<\/ul>\n\n\n\n<p><strong>Explanation<\/strong>: Reflecting over the yy-axis changes the sign of the xx-coordinates while leaving the yy-coordinates unchanged.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Problem 3: Rotation<\/h3>\n\n\n\n<p><strong>Original Figure<\/strong>: A pentagon with vertices W(1,1)W(1, 1), X(3,1)X(3, 1), Y(4,3)Y(4, 3), Z(2,4)Z(2, 4), V(0,3)V(0, 3).<br><strong>Transformation<\/strong>: Rotate 90\u00b0 counterclockwise around the origin.<\/p>\n\n\n\n<p><strong>Solution<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>W\u2032(\u22121,1)W'(-1, 1), X\u2032(\u22121,3)X'(-1, 3), Y\u2032(\u22123,4)Y'(-3, 4), Z\u2032(\u22124,2)Z'(-4, 2), V\u2032(\u22123,0)V'(-3, 0).<\/li>\n<\/ul>\n\n\n\n<p><strong>Explanation<\/strong>: For a 90\u00b0 counterclockwise rotation, (x,y)\u2192(\u2212y,x)(x, y) \\to (-y, x).<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Problem 4: Dilation<\/h3>\n\n\n\n<p><strong>Original Figure<\/strong>: A triangle with vertices A(2,2)A(2, 2), B(4,4)B(4, 4), C(6,2)C(6, 2).<br><strong>Transformation<\/strong>: Dilate by a factor of 0.5 centered at the origin.<\/p>\n\n\n\n<p><strong>Solution<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A\u2032(1,1)A'(1, 1), B\u2032(2,2)B'(2, 2), C\u2032(3,1)C'(3, 1).<\/li>\n<\/ul>\n\n\n\n<p><strong>Explanation<\/strong>: Multiply both xx- and yy-coordinates by the scale factor (0.5 in this case).<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Problem 5: Sequence of Reflections<\/h3>\n\n\n\n<p><strong>Original Figure<\/strong>: A square with vertices J(1,1)J(1, 1), K(3,1)K(3, 1), L(3,3)L(3, 3), M(1,3)M(1, 3).<br><strong>Transformation<\/strong>: Reflect over the xx-axis, then over the yy-axis.<\/p>\n\n\n\n<p><strong>Solution<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>After xx-axis: J\u2032(1,\u22121)J'(1, -1), K\u2032(3,\u22121)K'(3, -1), L\u2032(3,\u22123)L'(3, -3), M\u2032(1,\u22123)M'(1, -3).<\/li>\n\n\n\n<li>After yy-axis: J\u2032\u2032(\u22121,\u22121)J&#8221;(-1, -1), K\u2032\u2032(\u22123,\u22121)K&#8221;(-3, -1), L\u2032\u2032(\u22123,\u22123)L&#8221;(-3, -3), M\u2032\u2032(\u22121,\u22123)M&#8221;(-1, -3).<\/li>\n<\/ul>\n\n\n\n<p><strong>Explanation<\/strong>: Reflect over the xx-axis first (y\u2192\u2212yy \\to -y), then over the yy-axis (x\u2192\u2212xx \\to -x).<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Problem 6: Sequence of Translation and Rotation<\/h3>\n\n\n\n<p><strong>Original Figure<\/strong>: A parallelogram with vertices P(1,1)P(1, 1), Q(4,1)Q(4, 1), R(5,3)R(5, 3), S(2,3)S(2, 3).<br><strong>Transformation<\/strong>: Translate by (x,y)\u2192(x\u22122,y+3)(x, y) \\to (x &#8211; 2, y + 3), then rotate 180\u00b0 about the origin.<\/p>\n\n\n\n<p><strong>Solution<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>After translation: P\u2032(\u22121,4)P'(-1, 4), Q\u2032(2,4)Q'(2, 4), R\u2032(3,6)R'(3, 6), S\u2032(0,6)S'(0, 6).<\/li>\n\n\n\n<li>After rotation: P\u2032\u2032(1,\u22124)P&#8221;(1, -4), Q\u2032\u2032(\u22122,\u22124)Q&#8221;(-2, -4), R\u2032\u2032(\u22123,\u22126)R&#8221;(-3, -6), S\u2032\u2032(0,\u22126)S&#8221;(0, -6).<\/li>\n<\/ul>\n\n\n\n<p><strong>Explanation<\/strong>: Apply translation first, then for a 180\u00b0 rotation, change both signs ((x,y)\u2192(\u2212x,\u2212y)(x, y) \\to (-x, -y)).<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p>Graph each figure and its image step by step for a visual understanding of how the transformations are applied!<\/p>\n","protected":false},"excerpt":{"rendered":"<p>unit 9 transformations homework 7 sequences of transformations. directions: graph and label each figure and its image under the sequence of transformations. Give the coordinate of the image. i need 1-6 please The correct answer and explanation is: Sure, I&#8217;ll write out the steps and explanations for six problems involving sequences of transformations in geometry. [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-184977","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/184977","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=184977"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/184977\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=184977"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=184977"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=184977"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}