[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-467575-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-467575-en":130},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":74,"head_meta":76,"extra_data":78,"updated_unix":80},105,"en","rotating-around-axis-answer-key","Rotating Around Axis - Answer Key","","Rotating Around Axis answer key and solution guidance for a coordinate geometry worksheet. It uses the rotation angle θ and the rotation formulas x1 = x·cos(θ) − y·sin(θ) and y1 = x·sin(θ) + y·cos(θ). A worked example shows a point at (1,4) rotated by 60°, producing approximately (−2.98, 2.87). The answer section provides final coordinates for multiple rotation problems about the origin.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/exam/","Exam",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/rotating-around-axis-answer-key/467575/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/rotating-around-axis-answer-key/467575.png","ImageObject",300,407,{"name":42,"@type":43},"Asher","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-31","2026-09-30",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",5,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"What rotation formulas are used to find the new coordinates?","Question",{"text":63,"@type":64},"Use x1 = x·cos(θ) − y·sin(θ) and y1 = x·sin(θ) + y·cos(θ).","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"How is the example point (1,4) rotated by 60° solved?",{"text":68,"@type":64},"Substitute x = 1, y = 4, and θ = 60° into the formulas to get approximately (−2.98, 2.87).",{"name":70,"@type":61,"acceptedAnswer":71},"What do the worksheet answer problems require?",{"text":72,"@type":64},"Each problem asks to rotate a given shape by a specified angle (e.g., 91°, 189°, 140°, 202°) around the point (0,0) and report the resulting coordinates.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},467575,1792925438,{"code":4,"msg":82,"data":83},"success",[84,88,92,95,99,104,109,114,119,122,126],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":89,"show_sort_weight":90,"slug":91},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":93,"slug":94},70,"exam",{"id":55,"doc_module":4,"doc_module_name":25,"category_name":96,"show_sort_weight":97,"slug":98},"Comic",60,"comic",{"id":100,"doc_module":4,"doc_module_name":25,"category_name":101,"show_sort_weight":102,"slug":103},6,"Technology",50,"technology",{"id":105,"doc_module":4,"doc_module_name":25,"category_name":106,"show_sort_weight":107,"slug":108},7,"Healthcare",40,"healthcare",{"id":110,"doc_module":4,"doc_module_name":25,"category_name":111,"show_sort_weight":112,"slug":113},8,"Research & Report",30,"research-report",{"id":115,"doc_module":4,"doc_module_name":25,"category_name":116,"show_sort_weight":117,"slug":118},9,"Religion & Spirituality",20,"religion-spirituality",{"id":117,"doc_module":4,"doc_module_name":25,"category_name":120,"show_sort_weight":117,"slug":121},"World Cup","world-cup",{"id":123,"doc_module":4,"doc_module_name":25,"category_name":124,"show_sort_weight":123,"slug":125},10,"Lifestyle","lifestyle",{"id":127,"doc_module":4,"doc_module_name":25,"category_name":128,"show_sort_weight":55,"slug":129},19,"General","general",{"code":4,"msg":82,"data":131},{"doc_id":79,"user_id":132,"nickname":42,"user_avatar":133,"doc_module":4,"category_id":33,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":30,"language":139,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":12,"update_tm":143,"read_time":110},687197207639,"https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd","Rotating Around Axis  \nName:  \n\n| \u003Cbr>Rotate each shape. Answer with the new coordinates.\u003Cbr>θ = Angle of Rotation\u003Cbr>Rotation Formula\u003Cbr>x1 = x×cos(θ) -y×sin(θ)\u003Cbr>y1 = x×sin(θ) + y×cos(θ)\u003Cbr>In the example to the right the shape is at coordinates (1,4) . Lets find the coordinates if we rotated the shape 60° .\u003Cbr>\u003Cbr>1. x1 = 1×cos(60) -4×sin(60) y1 = 1×sin(60) + 4×cos(60)\u003Cbr>2. x1 = 1×0 .5-4×0 .87 y1 = 1×0.87 + 4×0.5\u003Cbr>3. x1 = 0.5-3.48 y1 = 0.87 + 2\u003Cbr>4. x1 = -2.98 y1 = 2.87\u003Cbr>5. Looking at shape, we can see that rotated 60° it is at\u003Cbr>(-2 .98 , 2 .87) .\u003Cbr>|  | Answers\u003Cbr>1.  \u003Cbr>2.  \u003Cbr>3.  \u003Cbr>4.   |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- |\n| 1) Rotate the shape-91° around the point (0,0) .\u003Cbr>\u003Cbr>II I\u003Cbr>III IV\u003Cbr>| 2) Rotate the shape-189° around the point (0,0) .\u003Cbr>\u003Cbr>II I\u003Cbr>III IV\u003Cbr>|  |  |  |  |  |\n| 3) Rotate the shape-140° around the point 4) Rotate the shape 202° around the point (0,0) . (0,0) .\u003Cbr>\u003Cbr>II I\u003Cbr>III IV\u003Cbr>\u003Cbr>\u003Cbr>II I\u003Cbr>III IV\u003Cbr>|  |  |  |  |  |  |\n|  |  |  |  |  |  |  |\n\n[Math](Math www.CommonCoreSheets.com 8 1-4)[ www.CommonCoreSheets.com](Math www.CommonCoreSheets.com 8 1-4)[ 8](Math www.CommonCoreSheets.com 8 1-4)[ 1-4](Math www.CommonCoreSheets.com 8 1-4) 75 50 25 0  \nRotating Around Axis  \nName: Answer Key  \n\n| \u003Cbr>Rotate each shape. Answer with the new coordinates.\u003Cbr>θ = Angle of Rotation\u003Cbr>Rotation Formula\u003Cbr>x1 = x×cos(θ) -y×sin(θ)\u003Cbr>y1 = x×sin(θ) + y×cos(θ)\u003Cbr>In the example to the right the shape is at coordinates (1,4) . Lets find the coordinates if we rotated the shape 60° .\u003Cbr>\u003Cbr>1. x1 = 1×cos(60) -4×sin(60) y1 = 1×sin(60) + 4×cos(60)\u003Cbr>2. x1 = 1×0 .5-4×0 .87 y1 = 1×0.87 + 4×0.5\u003Cbr>3. x1 = 0.5-3.48 y1 = 0.87 + 2\u003Cbr>4. x1 = -2.98 y1 = 2.87\u003Cbr>5. Looking at shape, we can see that rotated 60° it is at\u003Cbr>(-2 .98 , 2 .87) .\u003Cbr>|  | Answers 1.  (6.9,4.1) \u003Cbr>2.  (2.9,-5.6)  3.  (2.9,-1.2)  4.  (-5.2,3.2)  |\n| --- | --- | --- |\n| 1) Rotate the shape-91° around the point (0,0) .\u003Cbr>(4 )\u003Cbr>II I\u003Cbr>III IV\u003Cbr>| 2) Rotate the shape-189° around the point (0,0) .\u003Cbr>(- 2, -6 )\u003Cbr>II I\u003Cbr>III IV\u003Cbr>\u003Cbr>|  |\n| 3) Rotate the shape-140° around the point 4) Rotate the shape 202° around the point (0,0) . (0,0) . |  |  |\n| ( 3, 1)\u003Cbr>II I\u003Cbr>III IV\u003Cbr>\u003Cbr>(6 ) ,\u003Cbr>II I\u003Cbr>III IV\u003Cbr>\u003Cbr>1 |  |  |\n\n[www.CommonCoreSheets.com](www.CommonCoreSheets.com 8 1-4)[ 8](www.CommonCoreSheets.com 8 1-4)[ 1-4](www.CommonCoreSheets.com 8 1-4) 75 50 25 0  \nMath  \nRotating Around Axis  \nName:  \n\n| \u003Cbr>Rotate each shape. Answer with the new coordinates.\u003Cbr>θ = Angle of Rotation\u003Cbr>Rotation Formula\u003Cbr>x1 = x×cos(θ) -y×sin(θ)\u003Cbr>y1 = x×sin(θ) + y×cos(θ)\u003Cbr>In the example to the right the shape is at coordinates (1,4) . Lets find the coordinates if we rotated the shape 60° .\u003Cbr>\u003Cbr>1. x1 = 1×cos(60) -4×sin(60) y1 = 1×sin(60) + 4×cos(60)\u003Cbr>2. x1 = 1×0 .5-4×0 .87 y1 = 1×0.87 + 4×0.5\u003Cbr>3. x1 = 0.5-3.48 y1 = 0.87 + 2\u003Cbr>4. x1 = -2.98 y1 = 2.87\u003Cbr>5. Looking at shape, we can see that rotated 60° it is at\u003Cbr>(-2 .98 , 2 .87) .\u003Cbr>|  | Answers\u003Cbr>1.  \u003Cbr>2.   |  |  |\n| --- | --- | --- | --- | --- |\n| 1) Rotate the shape-91° around the point (0,0) .\u003Cbr>\u003Cbr>II I\u003Cbr>III IV\u003Cbr>| 2) Rotate the shape-189° around the point (0,0) .\u003Cbr>\u003Cbr>II I\u003Cbr>III IV\u003Cbr>|  |  |  |\n|  |  | 1-2 | 50 | 0 |\n\nMath  \nModified  \n[www.CommonCoreSheets.com](www.CommonCoreSheets.com)  \n8","cbCaidAq53eWh3u3","https://ap.wps.com/l/cbCaidAq53eWh3u3","pdf",55463,"English","# Rotate each shape\n## Rotation formula (x1, y1)\n## Example: rotate 60°\n## Answers for each problem","[{\"question\":\"What rotation formulas are used to find the new coordinates?\",\"answer\":\"Use x1 = x·cos(θ) − y·sin(θ) and y1 = x·sin(θ) + y·cos(θ).\"},{\"question\":\"How is the example point (1,4) rotated by 60° solved?\",\"answer\":\"Substitute x = 1, y = 4, and θ = 60° into the formulas to get approximately (−2.98, 2.87).\"},{\"question\":\"What do the worksheet answer problems require?\",\"answer\":\"Each problem asks to rotate a given shape by a specified angle (e.g., 91°, 189°, 140°, 202°) around the point (0,0) and report the resulting coordinates.\"}]","Rotating Around Axis - Answer Key | PDF",1790773028]