{"id":19998,"date":"2024-04-15T05:47:01","date_gmt":"2024-04-15T05:47:01","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=19998"},"modified":"2024-04-15T05:47:01","modified_gmt":"2024-04-15T05:47:01","slug":"the-figure-shows-a-shape-abc-and-its-mirror-image-a1b1c1-across-the-horizontal-axis-x-axis-the-coordinate-transformation-matrix-that-maps-abc-to-a1b1c1-is-a-left-beginarray20c-0","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/the-figure-shows-a-shape-abc-and-its-mirror-image-a1b1c1-across-the-horizontal-axis-x-axis-the-coordinate-transformation-matrix-that-maps-abc-to-a1b1c1-is-a-left-beginarray20c-0\/","title":{"rendered":"The figure shows a shape ABC and its mirror image A1B1C1 across the horizontal axis (X-axis). The coordinate transformation matrix that maps ABC to A1B1C1 is A. \\[\\left[ {\\begin{array}{*{20}{c}} 0&#038;1 \\\\ 1&#038;0 \\end{array}} \\right]\\] B. \\[\\left[ {\\begin{array}{*{20}{c}} 0&#038;1 \\\\ { &#8211; 1}&#038;0 \\end{array}} \\right]\\] C. \\[\\left[ {\\begin{array}{*{20}{c}} { &#8211; 1}&#038;0 \\\\ 0&#038;1 \\end{array}} \\right]\\] D. \\[\\left[ {\\begin{array}{*{20}{c}} 1&#038;0 \\\\ 0&#038;{ &#8211; 1} \\end{array}} \\right]\\]"},"content":{"rendered":"<p>[amp_mcq option1=&#8221;\\[\\left[ {\\begin{array}{*{20}{c}} 0&#038;1 \\\\ 1&#038;0 \\end{array}} \\right]\\]&#8221; option2=&#8221;\\[\\left[ {\\begin{array}{*{20}{c}} 0&#038;1 \\\\ { &#8211; 1}&#038;0 \\end{array}} \\right]\\]&#8221; option3=&#8221;\\[\\left[ {\\begin{array}{*{20}{c}} { &#8211; 1}&#038;0 \\\\ 0&#038;1 \\end{array}} \\right]\\]&#8221; option4=&#8221;\\[\\left[ {\\begin{array}{*{20}{c}} 1&#038;0 \\\\ 0&#038;{ &#8211; 1} \\end{array}} \\right]\\]&#8221; correct=&#8221;option1&#8243;]<!--more--><\/p>\n<p>The correct answer is $\\boxed{\\left[ {\\begin{array}{*{20}{c}} { &#8211; 1}&amp;0 \\ 0&amp;1 \\end{array}} \\right]}$.<\/p>\n<p>A coordinate transformation matrix is a matrix that maps points in one coordinate system to points in another coordinate system. In this case, we are interested in the coordinate transformation matrix that maps points in the original coordinate system (where shape ABC is located) to points in the reflected coordinate system (where shape A1B1C1 is located).<\/p>\n<p>The reflection across the horizontal axis (X-axis) is a linear transformation, which means that it can be represented by a matrix. The matrix that represents this transformation is a diagonal matrix with $-1$ on the diagonal. This is because the reflection across the horizontal axis maps each point $(x, y)$ to the point $(x, -y)$.<\/p>\n<p>Therefore, the coordinate transformation matrix that maps ABC to A1B1C1 is $\\boxed{\\left[ {\\begin{array}{*{20}{c}} { &#8211; 1}&amp;0 \\ 0&amp;1 \\end{array}} \\right]}$.<\/p>\n<p>Here is a brief explanation of each option:<\/p>\n<ul>\n<li>Option A: This matrix maps each point $(x, y)$ to the point $(x, y)$. This is not a reflection across the horizontal axis.<\/li>\n<li>Option B: This matrix maps each point $(x, y)$ to the point $(-x, y)$. This is a reflection across the vertical axis.<\/li>\n<li>Option C: This matrix maps each point $(x, y)$ to the point $(x, -y)$. This is the correct answer.<\/li>\n<li>Option D: This matrix maps each point $(x, y)$ to the point $(-x, -y)$. This is a reflection across both the horizontal and vertical axes.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>[amp_mcq option1=&#8221;\\[\\left[ {\\begin{array}{*{20}{c}} 0&#038;1 \\\\ 1&#038;0 \\end{array}} \\right]\\]&#8221; option2=&#8221;\\[\\left[ {\\begin{array}{*{20}{c}} 0&#038;1 \\\\ { &#8211; 1}&#038;0 \\end{array}} \\right]\\]&#8221; option3=&#8221;\\[\\left[ {\\begin{array}{*{20}{c}} { &#8211; 1}&#038;0 \\\\ 0&#038;1 \\end{array}} \\right]\\]&#8221; option4=&#8221;\\[\\left[ {\\begin{array}{*{20}{c}} 1&#038;0 \\\\ 0&#038;{ &#8211; 1} \\end{array}} \\right]\\]&#8221; correct=&#8221;option1&#8243;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[489],"tags":[],"class_list":["post-19998","post","type-post","status-publish","format-standard","hentry","category-linear-algebra","no-featured-image-padding"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.2 (Yoast SEO v23.3) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>The figure shows a shape ABC and its mirror image A1B1C1 across the horizontal axis (X-axis). The coordinate transformation matrix that maps ABC to A1B1C1 is A. \\[\\left[ {\\begin{array}{*{20}{c}} 0&amp;1 \\\\ 1&amp;0 \\end{array}} \\right]\\] B. \\[\\left[ {\\begin{array}{*{20}{c}} 0&amp;1 \\\\ { - 1}&amp;0 \\end{array}} \\right]\\] C. \\[\\left[ {\\begin{array}{*{20}{c}} { - 1}&amp;0 \\\\ 0&amp;1 \\end{array}} \\right]\\] D. \\[\\left[ {\\begin{array}{*{20}{c}} 1&amp;0 \\\\ 0&amp;{ - 1} \\end{array}} \\right]\\]<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/exam.pscnotes.com\/mcq\/the-figure-shows-a-shape-abc-and-its-mirror-image-a1b1c1-across-the-horizontal-axis-x-axis-the-coordinate-transformation-matrix-that-maps-abc-to-a1b1c1-is-a-left-beginarray20c-0\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"The figure shows a shape ABC and its mirror image A1B1C1 across the horizontal axis (X-axis). The coordinate transformation matrix that maps ABC to A1B1C1 is A. \\[\\left[ {\\begin{array}{*{20}{c}} 0&amp;1 \\\\ 1&amp;0 \\end{array}} \\right]\\] B. \\[\\left[ {\\begin{array}{*{20}{c}} 0&amp;1 \\\\ { - 1}&amp;0 \\end{array}} \\right]\\] C. \\[\\left[ {\\begin{array}{*{20}{c}} { - 1}&amp;0 \\\\ 0&amp;1 \\end{array}} \\right]\\] D. \\[\\left[ {\\begin{array}{*{20}{c}} 1&amp;0 \\\\ 0&amp;{ - 1} \\end{array}} \\right]\\]\" \/>\n<meta property=\"og:description\" content=\"[amp_mcq option1=&#8221;[left[ {begin{array}{*{20}{c}} 0&#038;1 \\ 1&#038;0 end{array}} right]]&#8221; option2=&#8221;[left[ {begin{array}{*{20}{c}} 0&#038;1 \\ { &#8211; 1}&#038;0 end{array}} right]]&#8221; option3=&#8221;[left[ {begin{array}{*{20}{c}} { &#8211; 1}&#038;0 \\ 0&#038;1 end{array}} right]]&#8221; option4=&#8221;[left[ {begin{array}{*{20}{c}} 1&#038;0 \\ 0&#038;{ &#8211; 1} end{array}} right]]&#8221; correct=&#8221;option1&#8243;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/the-figure-shows-a-shape-abc-and-its-mirror-image-a1b1c1-across-the-horizontal-axis-x-axis-the-coordinate-transformation-matrix-that-maps-abc-to-a1b1c1-is-a-left-beginarray20c-0\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2024-04-15T05:47:01+00:00\" \/>\n<meta name=\"author\" content=\"rawan239\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"rawan239\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"The figure shows a shape ABC and its mirror image A1B1C1 across the horizontal axis (X-axis). The coordinate transformation matrix that maps ABC to A1B1C1 is A. \\[\\left[ {\\begin{array}{*{20}{c}} 0&1 \\\\ 1&0 \\end{array}} \\right]\\] B. \\[\\left[ {\\begin{array}{*{20}{c}} 0&1 \\\\ { - 1}&0 \\end{array}} \\right]\\] C. \\[\\left[ {\\begin{array}{*{20}{c}} { - 1}&0 \\\\ 0&1 \\end{array}} \\right]\\] D. \\[\\left[ {\\begin{array}{*{20}{c}} 1&0 \\\\ 0&{ - 1} \\end{array}} \\right]\\]","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/exam.pscnotes.com\/mcq\/the-figure-shows-a-shape-abc-and-its-mirror-image-a1b1c1-across-the-horizontal-axis-x-axis-the-coordinate-transformation-matrix-that-maps-abc-to-a1b1c1-is-a-left-beginarray20c-0\/","og_locale":"en_US","og_type":"article","og_title":"The figure shows a shape ABC and its mirror image A1B1C1 across the horizontal axis (X-axis). The coordinate transformation matrix that maps ABC to A1B1C1 is A. \\[\\left[ {\\begin{array}{*{20}{c}} 0&1 \\\\ 1&0 \\end{array}} \\right]\\] B. \\[\\left[ {\\begin{array}{*{20}{c}} 0&1 \\\\ { - 1}&0 \\end{array}} \\right]\\] C. \\[\\left[ {\\begin{array}{*{20}{c}} { - 1}&0 \\\\ 0&1 \\end{array}} \\right]\\] D. \\[\\left[ {\\begin{array}{*{20}{c}} 1&0 \\\\ 0&{ - 1} \\end{array}} \\right]\\]","og_description":"[amp_mcq option1=&#8221;[left[ {begin{array}{*{20}{c}} 0&#038;1 \\ 1&#038;0 end{array}} right]]&#8221; option2=&#8221;[left[ {begin{array}{*{20}{c}} 0&#038;1 \\ { &#8211; 1}&#038;0 end{array}} right]]&#8221; option3=&#8221;[left[ {begin{array}{*{20}{c}} { &#8211; 1}&#038;0 \\ 0&#038;1 end{array}} right]]&#8221; option4=&#8221;[left[ {begin{array}{*{20}{c}} 1&#038;0 \\ 0&#038;{ &#8211; 1} end{array}} right]]&#8221; correct=&#8221;option1&#8243;]","og_url":"https:\/\/exam.pscnotes.com\/mcq\/the-figure-shows-a-shape-abc-and-its-mirror-image-a1b1c1-across-the-horizontal-axis-x-axis-the-coordinate-transformation-matrix-that-maps-abc-to-a1b1c1-is-a-left-beginarray20c-0\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2024-04-15T05:47:01+00:00","author":"rawan239","twitter_card":"summary_large_image","twitter_misc":{"Written by":"rawan239","Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/exam.pscnotes.com\/mcq\/the-figure-shows-a-shape-abc-and-its-mirror-image-a1b1c1-across-the-horizontal-axis-x-axis-the-coordinate-transformation-matrix-that-maps-abc-to-a1b1c1-is-a-left-beginarray20c-0\/","url":"https:\/\/exam.pscnotes.com\/mcq\/the-figure-shows-a-shape-abc-and-its-mirror-image-a1b1c1-across-the-horizontal-axis-x-axis-the-coordinate-transformation-matrix-that-maps-abc-to-a1b1c1-is-a-left-beginarray20c-0\/","name":"The figure shows a shape ABC and its mirror image A1B1C1 across the horizontal axis (X-axis). The coordinate transformation matrix that maps ABC to A1B1C1 is A. \\[\\left[ {\\begin{array}{*{20}{c}} 0&1 \\\\ 1&0 \\end{array}} \\right]\\] B. \\[\\left[ {\\begin{array}{*{20}{c}} 0&1 \\\\ { - 1}&0 \\end{array}} \\right]\\] C. \\[\\left[ {\\begin{array}{*{20}{c}} { - 1}&0 \\\\ 0&1 \\end{array}} \\right]\\] D. \\[\\left[ {\\begin{array}{*{20}{c}} 1&0 \\\\ 0&{ - 1} \\end{array}} \\right]\\]","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2024-04-15T05:47:01+00:00","dateModified":"2024-04-15T05:47:01+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/the-figure-shows-a-shape-abc-and-its-mirror-image-a1b1c1-across-the-horizontal-axis-x-axis-the-coordinate-transformation-matrix-that-maps-abc-to-a1b1c1-is-a-left-beginarray20c-0\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/the-figure-shows-a-shape-abc-and-its-mirror-image-a1b1c1-across-the-horizontal-axis-x-axis-the-coordinate-transformation-matrix-that-maps-abc-to-a1b1c1-is-a-left-beginarray20c-0\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/the-figure-shows-a-shape-abc-and-its-mirror-image-a1b1c1-across-the-horizontal-axis-x-axis-the-coordinate-transformation-matrix-that-maps-abc-to-a1b1c1-is-a-left-beginarray20c-0\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/exam.pscnotes.com\/mcq\/"},{"@type":"ListItem","position":2,"name":"mcq","item":"https:\/\/exam.pscnotes.com\/mcq\/category\/mcq\/"},{"@type":"ListItem","position":3,"name":"Linear Algebra","item":"https:\/\/exam.pscnotes.com\/mcq\/category\/mcq\/linear-algebra\/"},{"@type":"ListItem","position":4,"name":"The figure shows a shape ABC and its mirror image A1B1C1 across the horizontal axis (X-axis). The coordinate transformation matrix that maps ABC to A1B1C1 is A. \\[\\left[ {\\begin{array}{*{20}{c}} 0&#038;1 \\\\ 1&#038;0 \\end{array}} \\right]\\] B. \\[\\left[ {\\begin{array}{*{20}{c}} 0&#038;1 \\\\ { &#8211; 1}&#038;0 \\end{array}} \\right]\\] C. \\[\\left[ {\\begin{array}{*{20}{c}} { &#8211; 1}&#038;0 \\\\ 0&#038;1 \\end{array}} \\right]\\] D. \\[\\left[ {\\begin{array}{*{20}{c}} 1&#038;0 \\\\ 0&#038;{ &#8211; 1} \\end{array}} \\right]\\]"}]},{"@type":"WebSite","@id":"https:\/\/exam.pscnotes.com\/mcq\/#website","url":"https:\/\/exam.pscnotes.com\/mcq\/","name":"MCQ and Quiz for Exams","description":"","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/exam.pscnotes.com\/mcq\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"Person","@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209","name":"rawan239","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/761a7274f9cce048fa5b921221e7934820d74514df93ef195a9d22af0c1c9001?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/761a7274f9cce048fa5b921221e7934820d74514df93ef195a9d22af0c1c9001?s=96&d=mm&r=g","caption":"rawan239"},"sameAs":["https:\/\/exam.pscnotes.com"],"url":"https:\/\/exam.pscnotes.com\/mcq\/author\/rawan239\/"}]}},"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/19998","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/comments?post=19998"}],"version-history":[{"count":0,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/19998\/revisions"}],"wp:attachment":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/media?parent=19998"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/categories?post=19998"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/tags?post=19998"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}