{"id":253245,"date":"2025-07-12T01:36:56","date_gmt":"2025-07-12T01:36:56","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=253245"},"modified":"2025-07-12T01:36:59","modified_gmt":"2025-07-12T01:36:59","slug":"type-the-correct-answer-in-each-box","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/12\/type-the-correct-answer-in-each-box\/","title":{"rendered":"Type the correct answer in each box."},"content":{"rendered":"\n<p> Type the correct answer in each box. Use numerals instead of words. If necessary, use \/ for the fraction bar(s). In the given diagram,<br>is a right triangle with<br>. Segment RT is divided into 5 equal parts. R(4.3, 7.4) T(-8.5, -2.2) S(4.3, -2.2) The coordinates of point O are ( , ), and the coordinates of point M are ( , )<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/image-418.png\" alt=\"\" class=\"wp-image-253246\"\/><\/figure>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>R<\/strong>(4.3, 7.4)<\/li>\n\n\n\n<li><strong>T<\/strong>(-8.5, -2.2)<\/li>\n\n\n\n<li><strong>S<\/strong>(4.3, -2.2)<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Find the coordinates of point O.<\/h3>\n\n\n\n<p>From the image, we see that <strong>segment RT<\/strong> is divided into 5 equal parts. To find the coordinates of point <strong>O<\/strong>, we need to find the point that divides <strong>RT<\/strong> into these five equal segments.<\/p>\n\n\n\n<p>We can use the section formula to divide the segment in a ratio. Since point <strong>O<\/strong> is the first point dividing <strong>RT<\/strong>, this is the 1st point, and the ratio is 1:4. The section formula for dividing a line segment between two points <strong>(x\u2081, y\u2081)<\/strong> and <strong>(x\u2082, y\u2082)<\/strong> in the ratio m:n is: x=nx1+mx2m+n,y=ny1+my2m+nx = \\frac{n x_1 + m x_2}{m + n}, \\quad y = \\frac{n y_1 + m y_2}{m + n}x=m+nnx1\u200b+mx2\u200b\u200b,y=m+nny1\u200b+my2\u200b\u200b<\/p>\n\n\n\n<p>Using the given coordinates for points <strong>R<\/strong> and <strong>T<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>m=1,n=4m = 1, n = 4m=1,n=4<\/li>\n\n\n\n<li>x1=4.3,y1=7.4x_1 = 4.3, y_1 = 7.4&#215;1\u200b=4.3,y1\u200b=7.4<\/li>\n\n\n\n<li>x2=\u22128.5,y2=\u22122.2x_2 = -8.5, y_2 = -2.2&#215;2\u200b=\u22128.5,y2\u200b=\u22122.2<\/li>\n<\/ul>\n\n\n\n<p>Now, applying the formula: xO=4(4.3)+1(\u22128.5)4+1=17.2\u22128.55=8.75=1.74x_O = \\frac{4(4.3) + 1(-8.5)}{4 + 1} = \\frac{17.2 &#8211; 8.5}{5} = \\frac{8.7}{5} = 1.74xO\u200b=4+14(4.3)+1(\u22128.5)\u200b=517.2\u22128.5\u200b=58.7\u200b=1.74 yO=4(7.4)+1(\u22122.2)4+1=29.6\u22122.25=27.45=5.48y_O = \\frac{4(7.4) + 1(-2.2)}{4 + 1} = \\frac{29.6 &#8211; 2.2}{5} = \\frac{27.4}{5} = 5.48yO\u200b=4+14(7.4)+1(\u22122.2)\u200b=529.6\u22122.2\u200b=527.4\u200b=5.48<\/p>\n\n\n\n<p>Thus, the coordinates of point <strong>O<\/strong> are <strong>(1.74, 5.48)<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Find the coordinates of point M.<\/h3>\n\n\n\n<p>Point <strong>M<\/strong> is the midpoint of <strong>segment RT<\/strong>. We can use the midpoint formula: xM=xR+xT2,yM=yR+yT2x_M = \\frac{x_R + x_T}{2}, \\quad y_M = \\frac{y_R + y_T}{2}xM\u200b=2xR\u200b+xT\u200b\u200b,yM\u200b=2yR\u200b+yT\u200b\u200b<\/p>\n\n\n\n<p>Substituting the coordinates of <strong>R<\/strong> and <strong>T<\/strong>: xM=4.3+(\u22128.5)2=\u22124.22=\u22122.1x_M = \\frac{4.3 + (-8.5)}{2} = \\frac{-4.2}{2} = -2.1xM\u200b=24.3+(\u22128.5)\u200b=2\u22124.2\u200b=\u22122.1 yM=7.4+(\u22122.2)2=5.22=2.6y_M = \\frac{7.4 + (-2.2)}{2} = \\frac{5.2}{2} = 2.6yM\u200b=27.4+(\u22122.2)\u200b=25.2\u200b=2.6<\/p>\n\n\n\n<p>Thus, the coordinates of point <strong>M<\/strong> are <strong>(-2.1, 2.6)<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Coordinates of point <strong>O<\/strong>: <strong>(1.74, 5.48)<\/strong><\/li>\n\n\n\n<li>Coordinates of point <strong>M<\/strong>: <strong>(-2.1, 2.6)<\/strong><\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner9-110.jpeg\" alt=\"\" class=\"wp-image-253247\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Type the correct answer in each box. Use numerals instead of words. If necessary, use \/ for the fraction bar(s). In the given diagram,is a right triangle with. Segment RT is divided into 5 equal parts. R(4.3, 7.4) T(-8.5, -2.2) S(4.3, -2.2) The coordinates of point O are ( , ), and the coordinates of [&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-253245","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/253245","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=253245"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/253245\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=253245"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=253245"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=253245"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}