{"id":226,"date":"2022-04-13T10:23:27","date_gmt":"2022-04-13T10:23:27","guid":{"rendered":"http:\/\/10thclass.deltapublications.in\/?page_id=226"},"modified":"2025-01-31T09:40:29","modified_gmt":"2025-01-31T09:40:29","slug":"l-2-lengths-of-segments-on-number-lines","status":"publish","type":"page","link":"https:\/\/10thclass.deltapublications.in\/index.php\/l-2-lengths-of-segments-on-number-lines\/","title":{"rendered":"L.2 Lengths of segments on number lines"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong> Lengths of segments on number lines<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-link-color has-huge-font-size wp-elements-8550df6181cd5d83aa7a08ef336a4ca1\" style=\"color:#74008b\">Key Notes :<\/p>\n\n\n\n<p class=\"has-large-font-size\"><strong>If the coordinate of Y is x1 and the coordinate of Z is x2 ,then the length of YZ is YZ = |x2 \u2212 x1|.<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">Introduction:<\/h3>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li><strong>Number Lines:<\/strong> A visual representation of numbers placed in order on a straight line.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">Basic Concepts:<\/h3>\n\n\n\n<ol class=\"wp-block-list has-large-font-size\">\n<li><strong>Coordinates:<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>Every point on a number line has a unique coordinate.<\/li>\n\n\n\n<li>Positive numbers are to the right, and negative numbers are to the left of zero.<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list has-large-font-size\">\n<li><strong>Length of a Segment:<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>The distance between two points on a number line.<\/li>\n\n\n\n<li>Calculated by finding the absolute difference between the coordinates of the two points.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">Calculating Lengths:<\/h3>\n\n\n\n<ol class=\"wp-block-list has-large-font-size\">\n<li><strong>Formula:<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>Length=\u2223<em>a<\/em>\u2212<em>b<\/em>\u2223   where <em>a<\/em> and <em>b<\/em> are the coordinates of the endpoints.<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li class=\"has-large-font-size\"><strong>Examples:<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>If point <em>A<\/em> is at 3 and point <em>B<\/em> is at -2, the length of segment  <em>AB<\/em> is \u22233\u2212(\u22122)\u2223=5\u22233\u2212(\u22122)\u2223=5.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">Properties:<\/h3>\n\n\n\n<ol class=\"wp-block-list has-large-font-size\">\n<li><strong>Direction Matters:<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-large-font-size\">Length is always positive due to the absolute value.<\/li>\n\n\n\n<li class=\"has-large-font-size\">The order of the coordinates matters in the calculation.<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li class=\"has-large-font-size\"><strong>Zero Length:<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-large-font-size\">If (a = b), the length is zero as the points coincide.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">Applications:<\/h3>\n\n\n\n<ol class=\"wp-block-list has-large-font-size\">\n<li><strong>Real-world Examples:<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>Representing distances on a map.<\/li>\n\n\n\n<li>Measuring changes in temperature or stock prices over time.<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list has-large-font-size\">\n<li><strong>Problem Solving:<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>Solving problems involving distances and intervals on a number line.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">Conclusion:<\/h3>\n\n\n\n<p class=\"has-large-font-size\">Understanding the lengths of segments on number lines is fundamental in mathematics. It provides a visual and quantitative way to analyze distances and relationships between points. The concept is applicable in various fields and serves as a foundation for more advanced mathematical concepts.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"has-text-align-center has-text-color has-large-font-size\" style=\"color:#105000\"><strong>Learn with an example<\/strong><\/p>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#d4f2d4\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color has-link-color wp-elements-e41f16248db5edab6451654187a43741\" style=\"color:#b00012\"><strong> What is the length of <em>BC<\/em> ?<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"835\" height=\"100\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/11\/image-9.png\" alt=\"\" class=\"wp-image-9928\" style=\"aspect-ratio:8.35;width:501px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/11\/image-9.png 835w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/11\/image-9-300x36.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/11\/image-9-768x92.png 768w\" sizes=\"auto, (max-width: 835px) 100vw, 835px\" \/><\/figure>\n\n\n\n<p class=\"has-large-font-size\"><strong>If the coordinate of Y is x1 and  the coordinate of Z is x2 ,then the length of YZ is YZ = |x2 \u2212 x1|<\/strong>.<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-large-font-size\">Find the coordinates of&nbsp;B&nbsp;and&nbsp;C on the number line.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"835\" height=\"100\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-removebg-preview-2023-12-28T144119.699.png\" alt=\"\" class=\"wp-image-10863\" style=\"width:593px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-removebg-preview-2023-12-28T144119.699.png 835w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-removebg-preview-2023-12-28T144119.699-300x36.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-removebg-preview-2023-12-28T144119.699-768x92.png 768w\" sizes=\"auto, (max-width: 835px) 100vw, 835px\" \/><\/figure>\n\n\n\n<p class=\"has-large-font-size\">The coordinate of B is 86 and the coordinate of C is 88.The length of BC is the distance between B and C on the number line . To find BC plug B and C into the distance formula . So , BC = |88-86| = |2| = 2 .<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#dbdbea\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color has-link-color wp-elements-b3f7bb99a523b9bd3a9503080478511a\" style=\"color:#b00012\"><strong>What is the length of WX ?<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"761\" height=\"94\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-4.png\" alt=\"\" class=\"wp-image-10868\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-4.png 761w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-4-300x37.png 300w\" sizes=\"auto, (max-width: 761px) 100vw, 761px\" \/><\/figure>\n<\/div><\/div>\n\n\n\n<p>Find the coordinates of&nbsp;<em>W<\/em>&nbsp;and&nbsp;<em>X<\/em>&nbsp;on the number line.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"761\" height=\"94\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-removebg-preview-2023-12-28T145727.056.png\" alt=\"\" class=\"wp-image-10869\" style=\"width:583px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-removebg-preview-2023-12-28T145727.056.png 761w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-removebg-preview-2023-12-28T145727.056-300x37.png 300w\" sizes=\"auto, (max-width: 761px) 100vw, 761px\" \/><\/figure>\n\n\n\n<p>The coordinate of W  is 77 and the coordinate of X  is 79.The length of WX is the distance between W and X on the number line . To find WX  plug W and X into the distance formula . So , WX = |79-77| = |2| = 2 .<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#f6d6d6\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color has-link-color wp-elements-8d1617af8152bf8dd23fd0f57d8e31dd\" style=\"color:#b00012\"><strong>What is the length of GH?<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"741\" height=\"95\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-5.png\" alt=\"\" class=\"wp-image-10870\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-5.png 741w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-5-300x38.png 300w\" sizes=\"auto, (max-width: 741px) 100vw, 741px\" \/><\/figure>\n<\/div><\/div>\n\n\n\n<p>Find the coordinates of&nbsp;<em>G<\/em>&nbsp;and&nbsp;<em>H<\/em>&nbsp;on the number line.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"741\" height=\"95\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-removebg-preview-2023-12-28T150316.852.png\" alt=\"\" class=\"wp-image-10871\" style=\"width:593px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-removebg-preview-2023-12-28T150316.852.png 741w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-removebg-preview-2023-12-28T150316.852-300x38.png 300w\" sizes=\"auto, (max-width: 741px) 100vw, 741px\" \/><\/figure>\n\n\n\n<p>The coordinate of G  is 0 and the coordinate of H  is 2.The length of GH  is the distance between G and H on the number line . To find GH  plug G and H into the distance formula . So , GH= |2-0| = |2| = 2 .<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\"><strong>let&#8217;s practice!<\/strong><\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/85886\/054\/594\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-66.png\" alt=\"\" class=\"wp-image-7023\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-66.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-66-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-66-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/63829\/881\/760\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-84.png\" alt=\"\" class=\"wp-image-7025\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-84.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-84-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-84-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Lengths of segments on number lines Key Notes : If the coordinate of Y is x1 and the coordinate of Z is x2 ,then the length of YZ is YZ = |x2 \u2212 x1|. Introduction: Basic Concepts: Calculating Lengths: Properties: Applications: Conclusion: Understanding the lengths of segments on number lines is fundamental in mathematics. It<a class=\"more-link\" href=\"https:\/\/10thclass.deltapublications.in\/index.php\/l-2-lengths-of-segments-on-number-lines\/\">Continue reading <span class=\"screen-reader-text\">&#8220;L.2 Lengths of segments on number lines&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-226","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/226","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=226"}],"version-history":[{"count":15,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/226\/revisions"}],"predecessor-version":[{"id":17489,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/226\/revisions\/17489"}],"wp:attachment":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=226"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}