Which transformation would take Figure A to Figure B?<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n To determine which transformation takes Figure A<\/strong> to Figure B<\/strong>, let’s analyze each transformation option. Although we don\u2019t have a visual, we can logically break down each transformation to identify the correct one.<\/p>\n\n\n\n In coordinate geometry, transformations change a figure\u2019s position, orientation, or size. Common transformations include reflections, rotations, translations, and dilations. When evaluating which transformation takes Figure A to Figure B, we focus on how the figure’s points change between positions.<\/p>\n\n\n\n Let\u2019s look at the four options one by one:<\/p>\n\n\n\n A reflection over the line y = -x swaps the coordinates (x, y) to (\u2212y, \u2212x). For example, (2, 5) becomes (\u22125, \u22122). This transformation moves the figure diagonally to the opposite quadrant but also reverses both the x- and y-coordinates.<\/p>\n\n\n\n This might change the figure\u2019s orientation in a way that doesn\u2019t match Figure B if Figure B retains the relative orientation of Figure A.<\/p>\n\n\n\n A reflection over the line y = x swaps the x- and y-coordinates of each point. So, a point (x, y) becomes (y, x). For example, (3, 5) becomes (5, 3). This reflection flips the figure diagonally but maintains the same sign of each coordinate.<\/p>\n\n\n\n If Figure B appears to be a mirror image of Figure A across the line y = x, then this is the correct transformation. The structure and orientation of the figure will be preserved in a mirrored way across that line.<\/p>\n\n\n\n Rotating a figure 180\u00b0 clockwise (or counterclockwise\u2014it\u2019s the same for 180\u00b0) about the origin changes each point (x, y) to (\u2212x, \u2212y). This flips the figure to the opposite quadrant and reverses both coordinates. It doesn\u2019t produce a diagonal flip like a reflection would.<\/p>\n\n\n\n A 270\u00b0 clockwise rotation changes (x, y) to (y, \u2212x). This type of rotation moves the figure in a circular motion and alters its orientation significantly. It\u2019s not a simple mirror image.<\/p>\n\n\n\n Given the coordinate changes and the resulting orientation, the only transformation that preserves shape and mirrors it across a diagonal<\/strong> is:<\/p>\n\n\n\n \u2705 A reflection over the line y = x.<\/strong><\/p>\n<\/blockquote>\n","protected":false},"excerpt":{"rendered":" Which transformation would take Figure A to Figure B? The Correct Answer and Explanation is: To determine which transformation takes Figure A to Figure B, let’s analyze each transformation option. Although we don\u2019t have a visual, we can logically break down each transformation to identify the correct one. Correct Answer: A reflection over the line […]<\/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-216564","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/216564","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=216564"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/216564\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=216564"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=216564"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=216564"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n\n\n\nCorrect Answer: A reflection over the line y = x<\/strong><\/h3>\n\n\n\n
\n\n\n\nExplanation (300+ words):<\/strong><\/h3>\n\n\n\n
\n\n\n\n1. Reflection over the line y = -x:<\/strong><\/h4>\n\n\n\n
\n\n\n\n2. Reflection over the line y = x:<\/strong><\/h4>\n\n\n\n
\n\n\n\n3. Clockwise rotation of 180\u00b0 about the origin:<\/strong><\/h4>\n\n\n\n
\n\n\n\n4. Clockwise rotation of 270\u00b0 about the origin:<\/strong><\/h4>\n\n\n\n
\n\n\n\nConclusion:<\/strong><\/h3>\n\n\n\n
\n