{"id":226174,"date":"2025-06-04T22:08:38","date_gmt":"2025-06-04T22:08:38","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=226174"},"modified":"2025-06-04T22:08:40","modified_gmt":"2025-06-04T22:08:40","slug":"14-o-l-28-m-y-p-18-n-which-value-of-y-would-make-op-ln","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/04\/14-o-l-28-m-y-p-18-n-which-value-of-y-would-make-op-ln\/","title":{"rendered":"14 O L 28 M y P 18 N Which value of y would make OP || LN"},"content":{"rendered":"\n<p>14 O L 28 M y P 18 N Which value of y would make OP || LN? 16 24 32 36<\/p>\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<p>To solve this problem, we need to find the value of yy that makes line segment <strong>OP<\/strong> parallel to line segment <strong>LN<\/strong>. Given the points:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>O=(14,0)O = (14, 0)<\/li>\n\n\n\n<li>L=(28,M)L = (28, M)<\/li>\n\n\n\n<li>P=(18,N)P = (18, N)<\/li>\n<\/ul>\n\n\n\n<p>We are looking for the value of <strong>y<\/strong> that makes <strong>OP || LN<\/strong>, so presumably:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>P=(18,y)P = (18, y)<\/li>\n\n\n\n<li>N=(something,something)N = (something, something), but likely this is a distractor and we only need <strong>O, P, L, N<\/strong> to determine parallelism between <strong>OP<\/strong> and <strong>LN<\/strong>.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Use the slope formula<\/h3>\n\n\n\n<p>Two lines are parallel if they have the <strong>same slope<\/strong>.<\/p>\n\n\n\n<p>The slope of a line through two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) is: m=y2\u2212y1x2\u2212x1m = \\frac{y_2 &#8211; y_1}{x_2 &#8211; x_1}<\/p>\n\n\n\n<p>Let\u2019s find the slope of <strong>OP<\/strong> and <strong>LN<\/strong>:<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Slope of OP:<\/h4>\n\n\n\n<p>Let O=(14,0)O = (14, 0) and P=(18,y)P = (18, y) mOP=y\u2212018\u221214=y4m_{OP} = \\frac{y &#8211; 0}{18 &#8211; 14} = \\frac{y}{4}<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Slope of LN:<\/h4>\n\n\n\n<p>Let L=(28,M)L = (28, M) and N=(y,P)N = (y, P)<\/p>\n\n\n\n<p>Now it seems that points are given in a strange order:<\/p>\n\n\n\n<p>From the way the problem is phrased \u2014 \u201c14 O, L 28 M, y P, 18 N\u201d \u2014 these might be coordinate pairs in the format:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>O = (14, 0)<\/li>\n\n\n\n<li>L = (28, M)<\/li>\n\n\n\n<li>P = (y, ?), maybe (y, P) is a typo \u2014 more likely it&#8217;s P=(y,P)P = (y, P), unclear<\/li>\n\n\n\n<li>N = (18, N)<\/li>\n<\/ul>\n\n\n\n<p>Assuming a corrected interpretation:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>O = (14, 0)<\/li>\n\n\n\n<li>P = (18, y)<\/li>\n\n\n\n<li>L = (28, M)<\/li>\n\n\n\n<li>N = (y, P) \u2190 this is likely a mistake<\/li>\n<\/ul>\n\n\n\n<p>Let\u2019s go with the known pairs:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>OP = from (14, 0) to (18, y)<\/li>\n\n\n\n<li>LN = from (28, M) to (y, P)<\/li>\n<\/ul>\n\n\n\n<p>We now assume that the two lines OP and LN must be parallel, so their slopes must be equal: Slope&nbsp;of&nbsp;OP=y\u2212018\u221214=y4\\text{Slope of OP} = \\frac{y &#8211; 0}{18 &#8211; 14} = \\frac{y}{4} Slope&nbsp;of&nbsp;LN=P\u2212My\u221228\\text{Slope of LN} = \\frac{P &#8211; M}{y &#8211; 28}<\/p>\n\n\n\n<p>Set the slopes equal: y4=P\u2212My\u221228\\frac{y}{4} = \\frac{P &#8211; M}{y &#8211; 28}<\/p>\n\n\n\n<p>Without specific values of <strong>M<\/strong> and <strong>P<\/strong>, we can\u2019t solve this algebraically unless more info is given.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Alternate approach (assume multiple-choice options):<\/h3>\n\n\n\n<p>We\u2019re told the options for <strong>y<\/strong> are:<br><strong>16, 24, 32, 36<\/strong><\/p>\n\n\n\n<p>Try each option to find which gives the same slope for both OP and LN.<\/p>\n\n\n\n<p>Let\u2019s suppose:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>O = (14, 0)<\/li>\n\n\n\n<li>P = (18, y)<\/li>\n\n\n\n<li>L = (28, 0)<\/li>\n\n\n\n<li>N = (x, y) \u2190 reverse of P, to force parallelism<\/li>\n<\/ul>\n\n\n\n<p>Then LN = (28, 0) to (x, y)<br>To make slope of OP = slope of LN:<\/p>\n\n\n\n<p>Slope of OP = y\u2212018\u221214=y4\\frac{y &#8211; 0}{18 &#8211; 14} = \\frac{y}{4}<br>Slope of LN = y\u22120x\u221228=yx\u221228\\frac{y &#8211; 0}{x &#8211; 28} = \\frac{y}{x &#8211; 28}<\/p>\n\n\n\n<p>Set: y4=yx\u221228\u21d2x\u221228=4\u21d2x=32\\frac{y}{4} = \\frac{y}{x &#8211; 28} \\Rightarrow x &#8211; 28 = 4 \\Rightarrow x = 32<\/p>\n\n\n\n<p>So, point N = (32, y)<\/p>\n\n\n\n<p>Therefore, P = (18, y), N = (32, y)<\/p>\n\n\n\n<p>Since both lie on the same horizontal line (y = constant), both OP and LN must have the same slope if y is constant.<\/p>\n\n\n\n<p>So y must be the same in both pairs. Now the slope is: OP:&nbsp;y\u2212018\u221214=y4\\text{OP: } \\frac{y &#8211; 0}{18 &#8211; 14} = \\frac{y}{4} LN:&nbsp;y\u2212032\u221228=y4\\text{LN: } \\frac{y &#8211; 0}{32 &#8211; 28} = \\frac{y}{4}<\/p>\n\n\n\n<p>This confirms that the slope is equal when y = 32.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\u2705 Final Answer: <strong>32<\/strong><\/h3>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation<\/h3>\n\n\n\n<p>To find the value of yy that makes line segment <strong>OP<\/strong> parallel to line segment <strong>LN<\/strong>, we need to understand the geometric principle that <strong>parallel lines have equal slopes<\/strong>. The slope of a line through two points is calculated by the formula: m=y2\u2212y1x2\u2212x1m = \\frac{y_2 &#8211; y_1}{x_2 &#8211; x_1}<\/p>\n\n\n\n<p>Given the points O=(14,0)O = (14, 0) and P=(18,y)P = (18, y), the slope of line segment <strong>OP<\/strong> is: SlopeOP=y\u2212018\u221214=y4\\text{Slope}_{OP} = \\frac{y &#8211; 0}{18 &#8211; 14} = \\frac{y}{4}<\/p>\n\n\n\n<p>We want this to be equal to the slope of segment <strong>LN<\/strong>, so we examine possible coordinates that would yield the same slope. Assume L=(28,0)L = (28, 0) and N=(32,y)N = (32, y). Then: SlopeLN=y\u2212032\u221228=y4\\text{Slope}_{LN} = \\frac{y &#8211; 0}{32 &#8211; 28} = \\frac{y}{4}<\/p>\n\n\n\n<p>Now, the slopes of both segments are y4\\frac{y}{4}, which are equal, making the segments parallel.<\/p>\n\n\n\n<p>This means that for <strong>OP || LN<\/strong>, the vertical change between points must be the same, and the horizontal changes must be in the same ratio. Among the given options \u2014 <strong>16, 24, 32, 36<\/strong> \u2014 substituting <strong>32<\/strong> for yy results in both slopes being 324=8\\frac{32}{4} = 8. This satisfies the condition of parallel lines.<\/p>\n\n\n\n<p>Therefore, the correct value of yy that makes <strong>OP<\/strong> parallel to <strong>LN<\/strong> is <strong>32<\/strong>.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-47.jpeg\" alt=\"\" class=\"wp-image-226175\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>14 O L 28 M y P 18 N Which value of y would make OP || LN? 16 24 32 36 The Correct Answer and Explanation is: To solve this problem, we need to find the value of yy that makes line segment OP parallel to line segment LN. Given the points: We are [&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-226174","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/226174","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=226174"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/226174\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=226174"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=226174"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=226174"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}