[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-523066-105":59,"doc-detail-523066-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","coordinate-geometry-and-the-centroid-part-5-find-the-coordinates-of-the-centroid-of-each-triangle","Coordinate Geometry and the Centroid - Part 5 - Find the coordinates of the centroid of each triangle","","Coordinate Geometry and the Centroid worksheet focuses on finding each triangle’s centroid from given vertex coordinates. Multiple problems list three vertices for each triangle, requiring computation of the centroid coordinates. The set also includes critical thinking items that use midpoint connections to form a smaller triangle inside the original, asking for the smaller triangle’s centroid and an explanation of what changes. Answers emphasize centroid behavior under median construction.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/coordinate-geometry-and-the-centroid-part-5-find-the-coordinates-of-the-centroid-of-each-triangle/523066/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/coordinate-geometry-and-the-centroid-part-5-find-the-coordinates-of-the-centroid-of-each-triangle/523066.png","ImageObject",300,407,{"name":92,"@type":93},"Pentious","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-09","2026-10-08",true,{"@type":102,"interactionType":103,"userInteractionCount":44},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"How do you find the centroid when the three triangle vertices are given?","Question",{"text":112,"@type":113},"Use the centroid formula based on the three vertex coordinates. Compute the centroid’s x- and y-values from the listed points.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What is the centroid in the midpoint-constructed smaller triangle?",{"text":117,"@type":113},"The centroid stays the same because the medians do not change when midpoints of the sides are connected.",{"name":119,"@type":110,"acceptedAnswer":120},"Why doesn’t the centroid change after connecting the midpoints to form a smaller triangle?",{"text":121,"@type":113},"The medians remain the same lines in the original triangle’s geometry, so the intersection point (the centroid) is unchanged.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},523066,1791519370,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":44,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":19,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":143,"read_time":52,"preview_page_count":4},1374404730887,"https://ap-avatar.wpscdn.com/davatar_6f874abed73319feea01a86fa6f0fab8","Kuta Software-Infinite Geometry  \nCoordinate Geometry and the Centroid  \nFind coordinates of the centroid of each triangle.  \n1)  \n3)  \n5)  \n−7 −6 −5 −4 −3 −2 −1 Z  \n−7 −6 −5 −4 −3 −2 −1  \nQ  \n\n| |  |  |  |  |  |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n| | S | 5 |  |  |  |  |  |  |  |  |\n|  |  | 4 |  |  |  |  |  |  |  |  |\n|  |  | 3 |  |  |  |  |  |  |  |  |\n|  |  | 2 |  |  |  |  |  |  |  |  |\n|  |  | 1 |  |  |  |  |  |  |  |  |\n\n−2 −1 R 1 2 3 4 5 6 T 7  \nName   \nDate  Period   \n2)  \n4)  \n6)  \n−6 D−5 −4 −3 −2 −1 1 2 F 3  \n\n| L |  |  |  | K |  |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n| \u003Cbr>− | 3 − | 2 − | 1 |  | 1 2 | 3 | 4 | 5 | 6 |  |\n|  |  |  | −1 |  |  |  |  |  |  |  |\n|  |  |  | −2 |  |  |  |  |  |  |  |\n|  |  |  | −3 |  |  |  |  |  |  |  |\n|  |  |  | −4 |  |  |  |  |  |  |  |\n|  |  |  | −5 |  |  |  |  |  |  |  |\n|  |  |  | −6\u003Cbr>M |  |  |  |  |  |  |  |\n| −7 |  |  |  |  |  |  |  |  |  |  |\n\n7)  \n\n| |  |  |  |  |  |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n| |  |  |  |  | U |  |  |  |  |  |\n|  |  |  | 1 |  |  |  |  |  |  |  |\n| − | 3 − | 2 − | 1 |  | 1 2 | 3 | 4 | 5 | 6 |  |\n|  |  |  | −1 |  |  |  |  |  |  |  |\n|  |  |  | −2 |  |  |  |  |  |  |  |\n|  |  |  | −3 |  |  |  |  |  |  |  |\n|  | W |  | −4 |  |  |  |  |  | V |  |\n| −5 |  |  |  |  |  |  |  |  |  |  |\n\n2  \n8)  \nFind the coordinates of the centroid of each triangle given the three vertices.  \n9) C(−7, −6), B(−8, 0), A(0, 0) 10) S(0, −6), R(−10, −6), Q( 1, 0)  \n11) T(0, 0), U( 1, 3), V(−2, 0) 12) Y(3, 4), X(−5, 0), W(0, 0)  \n13) E(6, −3), D(−5, −3), C(6, −1) 14) F(−7, −3), G(−7, −5), H(−3, −3)  \nCritical thinking questions:  \n15) Two vertices of a triangle are (0, 0) and 16) For question \\#1, connect the midpoints of (9, 0) . The centroid is (6, 1) . Find the third each side of the triangle to form a smaller vertex of the triangle. triangle within the original triangle. Find  \nthe coordinates of the centroid of the  \nsmaller triangle. What happened and why?  \nKuta Software-Infinite Geometry Name   \nCoordinate Geometry and the Centroid Date  Period   \nFind coordinates of the centroid of each triangle.  \n1)  \n3)  \n5)  \n−7 −6 −5 −4 −3 −2 −1 Z  \n(−2, 1)  \n−7 −6 −5 −4 −3 −2 −1  \nQ  \n(−3, 4)  \n\n| |  |  |  |  |  |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n| | S | 5 |  |  |  |  |  |  |  |  |\n|  |  | 4 |  |  |  |  |  |  |  |  |\n|  |  | 3 |  |  |  |  |  |  |  |  |\n|  |  | 2 |  |  |  |  |  |  |  |  |\n|  |  | 1 |  |  |  |  |  |  |  |  |\n\n−2 −1 R 1 2 3 4 5 6 T 7  \n(~~ ~~53~~ ~~ , 43)  \n2)  \n4)  \n6)  \n−6 D−5 −4 −3 −2 −1 1 2 F 3  \n(−1, 2)  \n\n| L |  |  |  | K |  |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n| \u003Cbr>− | 3 − | 2 − | 1 |  | 1 2 | 3 | 4 | 5 | 6 |  |\n|  |  |  | −1 |  |  |  |  |  |  |  |\n|  |  |  | −2 |  |  |  |  |  |  |  |\n|  |  |  | −3 |  |  |  |  |  |  |  |\n|  |  |  | −4 |  |  |  |  |  |  |  |\n|  |  |  | −5 |  |  |  |  |  |  |  |\n|  |  |  | −6\u003Cbr>M |  |  |  |  |  |  |  |\n| −7 |  |  |  |  |  |  |  |  |  |  |\n\n( 1, −2)  \n(− ~~ ~~13~~ ~~ , − ~~ ~~43)  \n7)  \n\n| |  |  |  |  |  |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n| |  |  |  |  | U |  |  |  |  |  |\n|  |  |  | 1 |  |  |  |  |  |  |  |\n| − | 3 − | 2 − | 1 |  | 1 2 | 3 | 4 | 5 | 6 |  |\n|  |  |  | −1 |  |  |  |  |  |  |  |\n|  |  |  | −2 |  |  |  |  |  |  |  |\n|  |  |  | −3 |  |  |  |  |  |  |  |\n|  | W |  | −4 |  |  |  |  |  | V |  |\n| −5 |  |  |  |  |  |  |  |  |  |  |\n\n2  \n(~~ ~~43~~ ~~ , − ~~ ~~73)  \n8)  \n1 2 3 4 5 6 7 8  \n(3, ~~ ~~103~~ ~~ )  \nFind the coordinates of the centroid of each triangle given the three vertices.  \n9) C(−7, −6), B(−8, 0), A(0, 0)  \n(−5, −2)  \n11) T(0, 0), U( 1, 3), V(−2, 0)  \n(− ~~ ~~13~~ ~~ , 1)  \n13) E(6, −3), D(−5, −3), C(6, −1)  \n(~~ ~~73~~ ~~ , − ~~ ~~73)  \nCritical thinking questions:  \n15) Two vertices of a triangle are (0, 0) and (9, 0) . The","cbCaiqqrUC17CPNc","https://ap.wps.com/l/cbCaiqqrUC17CPNc","pdf",38787,"English","# Find the centroid of each triangle\n## Solve problems using given vertex coordinates\n# Critical thinking questions\n## Connect midpoints to form a smaller triangle","[{\"question\":\"How do you find the centroid when the three triangle vertices are given?\",\"answer\":\"Use the centroid formula based on the three vertex coordinates. Compute the centroid’s x- and y-values from the listed points.\"},{\"question\":\"What is the centroid in the midpoint-constructed smaller triangle?\",\"answer\":\"The centroid stays the same because the medians do not change when midpoints of the sides are connected.\"},{\"question\":\"Why doesn’t the centroid change after connecting the midpoints to form a smaller triangle?\",\"answer\":\"The medians remain the same lines in the original triangle’s geometry, so the intersection point (the centroid) is unchanged.\"}]","Coordinate Geometry and the Centroid - Part 5 - Find the coordinates of the centroid of each triangle | PDF",1791426458]