{"id":5014,"date":"2012-11-30T03:01:41","date_gmt":"2012-11-30T03:01:41","guid":{"rendered":"http:\/\/schooltutoring.com\/scholarship\/?p=5014"},"modified":"2014-12-02T08:31:55","modified_gmt":"2014-12-02T08:31:55","slug":"geometry-distance-formula","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/scholarship\/2012\/11\/30\/geometry-distance-formula\/","title":{"rendered":"Geometry: Distance Formula"},"content":{"rendered":"<p>Usually the coordinate place consists of two axes namely X axis and Y axis. Thus, a point in a coordinate plane is usually denoted by the coordinates (x,y) where x is the perpendicular distance of the point from Y-axis and y is the perpendicular distance from the X-axis as shown below.<\/p>\n<p><a href=\"https:\/\/SchoolTutoring.com\/wp-content\/uploads\/sites\/8\/2012\/11\/distanceformula1.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-5015\" title=\"distanceformula1\" src=\"https:\/\/SchoolTutoring.com\/wp-content\/uploads\/sites\/8\/2012\/11\/distanceformula1.jpg\" alt=\"\" width=\"185\" height=\"146\" \/><\/a><\/p>\n<p>Thus we can easily find the distance of a point from the axes just by seeing the x and y coordinates. But, how to find the distance between two points when their coordinates are given? We use Pythagoras theorem to find the distance between two points.<\/p>\n<p>Let P (x<sub>1<\/sub>,y<sub>1<\/sub>) and Q (x<sub>2<\/sub>,y<sub>2<\/sub>) be any two points in a plane. Let us find the distance between them PQ.<\/p>\n<p><a href=\"https:\/\/SchoolTutoring.com\/wp-content\/uploads\/sites\/8\/2012\/11\/distanceformula2.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-5016\" title=\"distanceformula2\" src=\"https:\/\/SchoolTutoring.com\/wp-content\/uploads\/sites\/8\/2012\/11\/distanceformula2.jpg\" alt=\"\" width=\"596\" height=\"413\" srcset=\"https:\/\/schooltutoring.com\/scholarship\/wp-content\/uploads\/sites\/8\/2012\/11\/distanceformula2.jpg 596w, https:\/\/schooltutoring.com\/scholarship\/wp-content\/uploads\/sites\/8\/2012\/11\/distanceformula2-300x207.jpg 300w\" sizes=\"auto, (max-width: 596px) 100vw, 596px\" \/><\/a><\/p>\n<p>Then from the figure, we get<\/p>\n<p>PR = |x<sub>2<\/sub>-x<sub>1<\/sub>| and QR = |y<sub>2<\/sub>-y<sub>1<\/sub>|.<\/p>\n<p>We know that the Pythagoras theorem states, \u201cIn a right angled triangle, the square of the hypotenuse is the sum of the squares of the other two sides\u201d.\u2019<\/p>\n<p>According to this theorem, we have<\/p>\n<p>PQ<sup>2<\/sup> = PR<sup>2<\/sup> + QR<sup>2<\/sup><\/p>\n<p>PQ<sup>2<\/sup> = |x<sub>2<\/sub>-x<sub>1<\/sub>| <sup>2<\/sup> + |y<sub>2<\/sub>-y<sub>1<\/sub>|.<sup>2<\/sup><\/p>\n<p>Taking square root on both sides, we get<\/p>\n<p>PQ = \u221a(|x<sub>2<\/sub>-x<sub>1<\/sub>| <sup>2<\/sup> + |y<sub>2<\/sub>-y<sub>1<\/sub>|<sup>2<\/sup>)<\/p>\n<p>We also offer Science tutoring, <a href=\"https:\/\/schooltutoring.com\/tutoring-programs\/science-tutoring\/\">click here<\/a> for more information.<\/p>\n<p><span class=\"tutorOrange\">SchoolTutoring Academy<\/span> is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Washington visit: <a href=\"https:\/\/schooltutoring.com\/Washington-Tutoring-Programs\/\">Tutoring in Washington.<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Usually the coordinate place consists of two axes namely X axis and Y axis. Thus, a point in a coordinate plane is usually denoted by the coordinates (x,y) where x is the perpendicular distance of the point from Y-axis and y is the perpendicular distance from the X-axis as shown below. Thus we can easily [&hellip;]<\/p>\n","protected":false},"author":19,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[10],"tags":[165,404,515,683,1349],"class_list":["post-5014","post","type-post","status-publish","format-standard","hentry","category-geometry","tag-axes","tag-coordiante-plane","tag-distance","tag-formula","tag-points"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/5014","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/users\/19"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/comments?post=5014"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/5014\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=5014"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=5014"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=5014"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}