[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-467568-105":3,"detail-sidebar-cat-0-en-105":80,"doc-detail-467568-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":73,"head_meta":75,"extra_data":77,"updated_unix":79},105,"en","rotating-around-axis-rotate-shapes-and-find-new-coordinates-angle-rotation-practice","Rotating Around Axis - Rotate Shapes and Find New Coordinates - Angle Rotation Practice","","Practice sheet for rotating shapes around the origin using a rotation angle. The document provides the rotation formula with cosine and sine terms, defines variables x1 and y1, and works through an example starting from coordinates (1,4) rotated by 60°. It then lists multiple problems requiring students to rotate shapes by specified degrees (e.g., 99°, -40°, -292°, 45°) and report the resulting coordinates, followed by an answer key.",{"@graph":14,"@context":72},[15,34,55],{"@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-rotate-shapes-and-find-new-coordinates-angle-rotation-practice/467568/",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-rotate-shapes-and-find-new-coordinates-angle-rotation-practice/467568.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":33},"InteractionCounter",{"@type":54},"ViewAction",{"@type":56,"mainEntity":57},"FAQPage",[58,64,68],{"name":59,"@type":60,"acceptedAnswer":61},"What rotation formula does the worksheet use to compute the new coordinates?","Question",{"text":62,"@type":63},"It uses x1 = x×cos(θ) − y×sin(θ) and y1 = x×sin(θ) + y×cos(θ) to find the rotated coordinates.","Answer",{"name":65,"@type":60,"acceptedAnswer":66},"How is the worksheet’s worked example performed for a 60° rotation?",{"text":67,"@type":63},"Starting from (1,4), it substitutes θ = 60° into the formula to compute x1 and y1, yielding approximately (-2.98, 2.87).",{"name":69,"@type":60,"acceptedAnswer":70},"What do the practice questions ask students to do?",{"text":71,"@type":63},"They rotate the given shape by specific angles around the point (0,0) and then provide the new coordinates as the answer.","https://schema.org",{"og:url":32,"og:type":74,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":76,"canonical":32},"index,follow",{"doc_id":78,"site_id":7},467568,1792925422,{"code":4,"msg":81,"data":82},"success",[83,87,91,94,99,104,109,114,119,122,126],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":84,"show_sort_weight":85,"slug":86},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":88,"show_sort_weight":89,"slug":90},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":92,"slug":93},70,"exam",{"id":95,"doc_module":4,"doc_module_name":25,"category_name":96,"show_sort_weight":97,"slug":98},5,"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":95,"slug":129},19,"General","general",{"code":4,"msg":81,"data":131},{"doc_id":78,"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":33,"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:  \nII I  \nIII IV  \nII I  \nIII IV  \nII I  \nIII IV  \nII I  \nIII IV  \nRotate each shape. Answer with the new coordinates.  \nθ = Angle of Rotation  \nRotation Formula  \nx1 = x×cos(θ) -y×sin(θ)  \ny1 = x×sin(θ) + y×cos(θ)  \nIn the example to the right the shape is at coordinates (1,4) . Lets find the coordinates if we rotated the shape 60° .  \n1. x1 = 1×cos(60) -4×sin(60) y1 = 1×sin(60) + 4×cos(60)  \n2. x1 = 1×0 .5-4×0 .87 y1 = 1×0.87 + 4×0.5  \n3. x1 = 0.5-3.48 y1 = 0.87 + 2  \n4. x1 = -2.98 y1 = 2.87  \n5. Looking at shape, we can see that rotated 60° it is at  \n(-2 .98 , 2 .87) .  \nAnswers  \n1.  \n2.  \n3.  \n4.  \n1) Rotate the shape 99° around the point (0,0) .  \n2) Rotate the shape-40° around the point (0,0) .  \n3) Rotate the shape-292° around the point 4) Rotate the shape 45° around the point (0,0) . (0,0) .  \n[Math](Math www.CommonCoreSheets.com 6 1-4)[ www.CommonCoreSheets.com](Math www.CommonCoreSheets.com 6 1-4)[ 6](Math www.CommonCoreSheets.com 6 1-4)[ 1-4](Math www.CommonCoreSheets.com 6 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.  (6.3,-5) \u003Cbr>2.  (9.9,-0.9)  3.  (5.6,-3.1)  4.  (-0.7,2.1)  |\n| --- | --- | --- |\n| 1) Rotate the shape 99° around the point (0,0) .\u003Cbr>(4 - 7) ,\u003Cbr>II I\u003Cbr>III IV\u003Cbr>| 2) Rotate the shape-40° around the point (0,0) .\u003Cbr>|  |\n| 3) Rotate the shape-292° around the point 4) Rotate the shape 45° around the point (0,0) . (0,0) .\u003Cbr>5,- 4)\u003Cbr>II I\u003Cbr>III IV\u003Cbr>\u003Cbr>(- 2, -1 )\u003Cbr>II I\u003Cbr>III IV\u003Cbr>\u003Cbr>|  |  |\n\n[www.CommonCoreSheets.com](www.CommonCoreSheets.com 6 1-4)[ 6](www.CommonCoreSheets.com 6 1-4)[ 1-4](www.CommonCoreSheets.com 6 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 99° around the point (0,0) .\u003Cbr>\u003Cbr>II I\u003Cbr>III IV\u003Cbr>| 2) Rotate the shape-40° around the point (0,0) .\u003Cbr>|  |\n\nMath  \nModified  \n[www.CommonCoreSheets.com](www.CommonCoreSheets.com)  \n6  \n1-2 50 0  \n\n|  |  |\n| --- | --- |","cbCaisuw0ojsxBWu","https://ap.wps.com/l/cbCaisuw0ojsxBWu","pdf",55427,"English","# Rotation Formula\n## Example Rotation (60°)\n## Practice Problems (99°, -40°, -292°, 45°)\n## Answers","[{\"question\":\"What rotation formula does the worksheet use to compute the new coordinates?\",\"answer\":\"It uses x1 = x×cos(θ) − y×sin(θ) and y1 = x×sin(θ) + y×cos(θ) to find the rotated coordinates.\"},{\"question\":\"How is the worksheet’s worked example performed for a 60° rotation?\",\"answer\":\"Starting from (1,4), it substitutes θ = 60° into the formula to compute x1 and y1, yielding approximately (-2.98, 2.87).\"},{\"question\":\"What do the practice questions ask students to do?\",\"answer\":\"They rotate the given shape by specific angles around the point (0,0) and then provide the new coordinates as the answer.\"}]","Rotating Around Axis - Rotate Shapes and Find New Coordinates - Angle Rotation Practice | PDF",1790773015]