{"id":734549,"date":"2024-09-21T16:03:52","date_gmt":"2024-09-21T10:33:52","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/?p=734549"},"modified":"2024-09-21T16:03:52","modified_gmt":"2024-09-21T10:33:52","slug":"dilation","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/dilation\/","title":{"rendered":"Dilation"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/dilation\/#Definition_of_Dilation\" title=\"Definition of Dilation\">Definition of Dilation<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/dilation\/#Centre_of_Dilation\" title=\"Centre of Dilation\">Centre of Dilation<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/dilation\/#The_Scale_Factor\" title=\"The Scale Factor\">The Scale Factor<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/dilation\/#Scale_Factor_Formula\" title=\"Scale Factor Formula\">Scale Factor Formula<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/dilation\/#Dilation_in_Geometry\" title=\"Dilation in Geometry\">Dilation in Geometry<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/dilation\/#How_to_Calculate_the_Scale_Factor_in_Dilation\" title=\"How to Calculate the Scale Factor in Dilation?\">How to Calculate the Scale Factor in Dilation?<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/dilation\/#Important_Properties_Of_Dilation\" title=\"Important Properties Of Dilation\">Important Properties Of Dilation<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/dilation\/#Dilation_FAQs\" title=\"Dilation FAQs\">Dilation FAQs<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/dilation\/#What_is_dilation_in_mathematics\" title=\"What is dilation in mathematics? \">What is dilation in mathematics? <\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/dilation\/#How_do_you_calculate_the_scale_factor_in_dilation\" title=\"How do you calculate the scale factor in dilation? \">How do you calculate the scale factor in dilation? <\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/dilation\/#What_properties_remain_unchanged_after_dilation\" title=\" What properties remain unchanged after dilation? \"> What properties remain unchanged after dilation? <\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<p>Dilation refers to resizing an object while maintaining its shape. The size can be increased or decreased depending on the scale factor. Dilation in mathematics is used in geometry to enlarge or shrink two-dimensional and three-dimensional shapes while preserving their proportions. For example, a square with sides of 4 units can be dilated to a square with sides of 40 units, but its shape remains unchanged.<\/p>\n<p>In this article, we will learn more about Dilation, examples of Dilation and more.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Definition_of_Dilation\"><\/span>Definition of Dilation<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Dilation is a geometric transformation that resizes an object by either enlarging or shrinking it, based on a given scale factor. The result is a new figure called the image, while the original figure is called the pre-image.<\/p>\n<p><img loading=\"lazy\" class=\"size-full wp-image-734553 aligncenter\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2024\/09\/Dilation.jpg\" alt=\"Dilation\" width=\"451\" height=\"241\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2024\/09\/Dilation.jpg 451w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2024\/09\/Dilation-300x160.jpg 300w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2024\/09\/Dilation-150x80.jpg 150w\" sizes=\"(max-width: 451px) 100vw, 451px\" \/><\/p>\n<p><strong>There are two types of dilation:<\/strong><\/p>\n<ul>\n<li><strong>Expansion:<\/strong> When the size of the object increases, the object is said to be expanded.<\/li>\n<li><strong>Contraction:<\/strong> When the size of the object decreases, the object is said to be contracted.<\/li>\n<\/ul>\n<p>In both cases, the shape of the object remains unchanged.<\/p>\n<p>For example, if a square undergoes dilation, its size may increase or decrease, but its proportions and shape stay consistent.<\/p>\n<div class=\"card\" style=\"text-align: center;\"><a class=\"btn btn-primary\" href=\"https:\/\/infinitylearn.com\/one-stop-solutions-for-school-prep?utm_source=surge&amp;utm_medium=interlinking\"><br \/>\n<img loading=\"lazy\" class=\" lazyloaded\" style=\"width: 100%; border-radius: 10px;\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2024\/09\/one-stop-solution-for-school-exam.jpg\" alt=\"one-stop-solutions school exam\" width=\"1201\" height=\"636\" data-src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2024\/09\/one-stop-solution-for-school-exam.jpg\" \/><\/a><a class=\"btn btn-primary\" href=\"https:\/\/infinitylearn.com\/one-stop-solutions-for-school-prep?utm_source=surge&amp;utm_medium=interlinking\"><button><strong>One Stop Solutions for School Exam Preparation<\/strong><\/button><\/a><\/p>\n<div style=\"text-align: center;\">Boost your school preparation with our comprehensive guide for CBSE, ICSE, and State Board exams. Get all the resources you need in one place and excel in your academic journey. Discover the ultimate one-stop solution at Infinity Learn today!<\/div>\n<\/div>\n<h2><span class=\"ez-toc-section\" id=\"Centre_of_Dilation\"><\/span>Centre of Dilation<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>In dilation geometry, the centre of dilation is a key concept. It is the point from which the figure expands or contracts. The resizing of the object occurs relative to this point. If a figure is enlarged or reduced, it stretches or shrinks from the centre of dilation. For example, in a dilation of a triangle, the enlargement or reduction happens from the centre of dilation, marked as point &#8216;R&#8217; in the figure.<\/p>\n<p><img loading=\"lazy\" class=\"size-full wp-image-734554 aligncenter\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2024\/09\/Centre-of-Dilation-.jpg\" alt=\"Centre of Dilation \" width=\"385\" height=\"219\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2024\/09\/Centre-of-Dilation-.jpg 385w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2024\/09\/Centre-of-Dilation--300x171.jpg 300w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2024\/09\/Centre-of-Dilation--150x85.jpg 150w\" sizes=\"(max-width: 385px) 100vw, 385px\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"The_Scale_Factor\"><\/span>The Scale Factor<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The scale factor is the value used to resize a geometric figure in relation to its original size. It represents the ratio between the dimensions of the original figure and the dilated figure.<\/p>\n<ul>\n<li>If the scale factor (k) is greater than 1 (k &gt; 1), the image enlarges.<\/li>\n<li>If the scale factor is between 0 and 1 (0 &lt; k &lt; 1), the image contracts.<\/li>\n<li>If the scale factor is 1 (k = 1), the image remains the same size.<\/li>\n<li>The scale factor cannot be zero, and its magnitude determines the extent of dilation.<\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"Scale_Factor_Formula\"><\/span>Scale Factor Formula<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The scale factor can enlarge or shrink an object. The basic formula to calculate the scale factor of a dilated figure is:<\/p>\n<ul>\n<li>Scale factor = Dimension of the new shape\/Dimension of the original shape<\/li>\n<li>Alternatively, to find the dimensions of the new shape, you can also use the following formula:<\/li>\n<li>Dimensions of the original shape \u00d7 Scale factor = Dimension of the new shape<\/li>\n<li>This formula helps determine the size of the dilated figure based on the scale factor.<\/li>\n<\/ul>\n<div class=\"card\" style=\"text-align: center;\"><a class=\"btn btn-primary\" href=\"https:\/\/infinitylearn.com\/online-mock-tests?utm_source=surge&amp;utm_medium=interlinking\"><br \/>\n<img loading=\"lazy\" class=\" lazyloaded\" style=\"width: 100%; border-radius: 10px;\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2024\/09\/cvc.png\" alt=\"online mock test\" width=\"1201\" height=\"636\" data-src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2024\/09\/cvc.png\" \/><\/a><a class=\"btn btn-primary\" href=\"https:\/\/infinitylearn.com\/online-mock-tests?utm_source=surge&amp;utm_medium=interlinking\"><button><strong>Online Mock Test<\/strong><\/button><\/a><\/p>\n<div style=\"text-align: center;\">Boost Your Preparation With Our Free Online Mock Tests For IIT-JEE, NEET And CBSE Exams<\/div>\n<\/div>\n<h2><span class=\"ez-toc-section\" id=\"Dilation_in_Geometry\"><\/span>Dilation in Geometry<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Dilation in mathematics is the process of resizing an object or shape without altering its proportions or angles. The shape, whether it&#8217;s a point, line segment, polygon, etc., can be either enlarged or shrunk. However, the key feature of dilation is that the dimensions of the shape change uniformly, ensuring that its overall proportions and angles remain consistent.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"How_to_Calculate_the_Scale_Factor_in_Dilation\"><\/span>How to Calculate the Scale Factor in Dilation?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Use the original dimension and the modified dimension which then allows for assessment of a scaling factor. Let us work out a triangle\u2019s scaling factor given its original dimensions and enlarged measurements.<\/p>\n<p><img loading=\"lazy\" class=\"size-full wp-image-734557 aligncenter\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2024\/09\/Scale-Factor-in-Dilation.jpg\" alt=\"How to Calculate the Scale Factor in Dilation?\" width=\"229\" height=\"226\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2024\/09\/Scale-Factor-in-Dilation.jpg 229w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2024\/09\/Scale-Factor-in-Dilation-96x96.jpg 96w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2024\/09\/Scale-Factor-in-Dilation-150x148.jpg 150w\" sizes=\"(max-width: 229px) 100vw, 229px\" \/><\/p>\n<p>From the above figure, dilation lead to new coordinates of \u0394PQR given as follows:<\/p>\n<ul>\n<li>P(1,3) \u2192 P&#8217; (3,9)<\/li>\n<li>Q(3,1) \u2192 Q&#8217; (9,3)<\/li>\n<li>R(1,1) \u2192 R&#8217; (3,3)<\/li>\n<\/ul>\n<p>Now we can explore each point carefully:<\/p>\n<ul>\n<li><strong>Vertex P:<\/strong><\/li>\n<\/ul>\n<p>The x-coordinate 1 transformed to be 3 while the y-coordinate 3 transformed to be 9. This proves that both of P&#8217;s coordinates had their values triplicated in P&#8217;.<\/p>\n<ul>\n<li><strong>Vertex Q:<\/strong><\/li>\n<\/ul>\n<p>Contrarily, x-coordinate 3 turned into 9 whereas y-coordinate 1 became 3. This shows that there was the same relationship existing between Q and Q&#8217;.<\/p>\n<ul>\n<li><strong>Vertex R:<\/strong><\/li>\n<\/ul>\n<p>The x-coordinate 1 converted to 3 and y-coordinate 1 transformed to be 3 as well. Hence it can be depicted here in that both the position of R&#8217;s coordinates had their values of those locations multiplied by three times that of R&#8217;.<\/p>\n<p>Thus, this dilation has a scale factor of 3. To create the enlarged \u0394 PQR&#8217;, every coordinate of \u0394PQR is multiplied by the scale factor 3. In other words, if k is the scale factor, then (x,y) changes to (kx, ky).<\/p>\n<p><strong>The scale factor can also be computed simply using the formula: <\/strong><\/p>\n<p>Scale factor = Dimension of new shape \u00f7 Dimension of the original shape<\/p>\n<p>Hence, in this instance, we can find the scale factor by dividing coordinates of new vertices with the coordinates of original vertices.<\/p>\n<p><strong>Let\u2019s take dimensions of vertex P (1, 3) and P\u2019 (3,9).<\/strong><\/p>\n<ul>\n<li>Take the x-coordinate of P\u2019 = 3 and that of P = 1.<\/li>\n<li>Put them into the formula: 3 \u00f7 1 = 3.<\/li>\n<li>Now, consider the y-coordinate of P\u2019 = 9 and that of P = 3.<\/li>\n<li>Then, apply to it the same formula 9 \u00f7 3 = 3.<\/li>\n<li>Therefore, we have a scale factor of 3 for both coordinates.<\/li>\n<\/ul>\n<h3><span class=\"ez-toc-section\" id=\"Important_Properties_Of_Dilation\"><\/span>Important Properties Of Dilation<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Dilation in geometry preserves certain properties of the original figure while resizing it. Here are a few key properties that remain unchanged:<\/p>\n<ul>\n<li><strong>Perpendicular and Parallel Lines:<\/strong> The relationships between perpendicular and parallel lines in the original figure are maintained in the dilated image. If lines were parallel or perpendicular before dilation, they remain so afterwards.<\/li>\n<li><strong>Midpoints of Sides:<\/strong> The midpoints of the sides of the dilated figure correspond to the midpoints of the sides of the original figure. This means that if you find the midpoint of a side in the original shape, the same midpoint relationship will hold in the dilated shape.<\/li>\n<li><strong>Angles:<\/strong> The angles in the dilated image are equal to the angles in the original figure. The dilation does not alter the measure of any angle in the figure.<\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"Dilation_FAQs\"><\/span>Dilation FAQs<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"What_is_dilation_in_mathematics\"><\/span>What is dilation in mathematics? <span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tDilation is a geometric transformation that resizes a shape without changing its proportions or angles. It involves enlarging or shrinking the shape based on a scale factor. \t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"How_do_you_calculate_the_scale_factor_in_dilation\"><\/span>How do you calculate the scale factor in dilation? <span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tThe scale factor is calculated by dividing the dimension of the new shape by the dimension of the original shape. For example, if a shape\u2019s side length increases from 4 units to 8 units, the scale factor is 8\/4 = 2. \t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"What_properties_remain_unchanged_after_dilation\"><\/span> What properties remain unchanged after dilation? <span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tAfter dilation, the relationships between parallel and perpendicular lines, midpoints of sides, and the measures of angles remain unchanged. Only the size of the shape changes. \t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\n<script type=\"application\/ld+json\">\n\t{\n\t\t\"@context\": \"https:\/\/schema.org\",\n\t\t\"@type\": \"FAQPage\",\n\t\t\"mainEntity\": [\n\t\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"What is dilation in mathematics? \",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"Dilation is a geometric transformation that resizes a shape without changing its proportions or angles. It involves enlarging or shrinking the shape based on a scale factor.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"How do you calculate the scale factor in dilation? \",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"The scale factor is calculated by dividing the dimension of the new shape by the dimension of the original shape. For example, if a shape\u2019s side length increases from 4 units to 8 units, the scale factor is 8\/4 = 2.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \" What properties remain unchanged after dilation? \",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"After dilation, the relationships between parallel and perpendicular lines, midpoints of sides, and the measures of angles remain unchanged. Only the size of the shape changes.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t\t\t\t]\n\t}\n<\/script>\n\n","protected":false},"excerpt":{"rendered":"<p>Dilation refers to resizing an object while maintaining its shape. The size can be increased or decreased depending on the [&hellip;]<\/p>\n","protected":false},"author":53,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Dilation","_yoast_wpseo_title":"How to Calculate Dilation - Definition, Formula, Important Properties","_yoast_wpseo_metadesc":"Dilation refers to resizing an object while maintaining its shape. The size can be increased or decreased depending on the scale factor.","custom_permalink":"maths\/dilation\/"},"categories":[13],"tags":[],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>How to Calculate Dilation - Definition, Formula, Important Properties<\/title>\n<meta name=\"description\" content=\"Dilation refers to resizing an object while maintaining its shape. 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