[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-467566-105":59,"doc-detail-467566-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","rotating-around-axis-answer-key-rotate-each-shape-with-new-coordinates","Rotating Around Axis - Answer Key - Rotate Each Shape with New Coordinates","","Worksheet answer key for rotating shapes about an axis using coordinate geometry. Provides the rotation angle notation (θ), the rotation formulas x1 = x·cos(θ) − y·sin(θ) and y1 = x·sin(θ) + y·cos(θ), and works through an example rotating a point (1,4) by 60°. Includes calculated rotated coordinates for multiple problems and specific tasks rotating shapes by angles like 157°, 182°, 172°, and 303° about the origin.",{"@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/rotating-around-axis-answer-key-rotate-each-shape-with-new-coordinates/467566/",{"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/rotating-around-axis-answer-key-rotate-each-shape-with-new-coordinates/467566.png","ImageObject",300,407,{"name":92,"@type":93},"Asher","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-31","2026-09-30",true,{"@type":102,"interactionType":103,"userInteractionCount":81},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What rotation formulas are used to find the new coordinates?","Question",{"text":112,"@type":113},"The document uses x1 = x·cos(θ) − y·sin(θ) and y1 = x·sin(θ) + y·cos(θ). These convert an original point (x, y) into a rotated point (x1, y1).","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How does the example rotate the point (1,4) by 60°?",{"text":117,"@type":113},"It substitutes θ = 60° into the formulas to compute x1 and y1. The resulting location is shown as approximately (-2.98, 2.87).",{"name":119,"@type":110,"acceptedAnswer":120},"What kinds of rotation problems are included in the answer key?",{"text":121,"@type":113},"The answer key lists multiple items asking to rotate shapes by specific angles (such as 157°, 182°, 172°, and 303°) around a reference point, including the origin (0,0).","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},467566,1792898175,{"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":81,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":81,"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":39},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 157° around the point (0,0) .  \n2) Rotate the shape 182° around the point (0,0) .  \n3) Rotate the shape-172° around the point 4) Rotate the shape 303° around the point  \n(0,0) . (0,0) .  \n1-4 75 50 25 0  \n[www.CommonCoreSheets.com](www.CommonCoreSheets.com)  \nMath  \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.  (1.7,-1.5) \u003Cbr>2.  (2.1,3.9)  3.  (0,7.1)  4.  (2.3,-3.9)  |\n| --- | --- | --- |\n| 1) Rotate the shape 157° around the point (0,0) .\u003Cbr>(- 1, -2 )\u003Cbr>II I\u003Cbr>III IV\u003Cbr>\u003Cbr>| 2) Rotate the shape 182° around the point (0,0) .\u003Cbr>|  |\n| 3) Rotate the shape-172° around the point 4) Rotate the shape 303° around the point (0,0) . (0,0) . |  |  |\n| \u003Cbr>(- 2, 4)\u003Cbr>II I\u003Cbr>III IV\u003Cbr>\u003Cbr>|  |  |\n\nMath  \nSeed: 1879047481-82  \n[www.CommonCoreSheets.com](www.CommonCoreSheets.com)  \n1-4 75 50 25 0  \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 157° around the point (0,0) .\u003Cbr>\u003Cbr>II I\u003Cbr>III IV\u003Cbr>| 2) Rotate the shape 182° 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)","cbCaiortS2DDi1KR","https://ap.wps.com/l/cbCaiortS2DDi1KR","pdf",55403,"English","# Rotate Each Shape with New Coordinates\n## Rotation Angle and Formula\n## Example: Rotate (1,4) by 60°\n## Answers for Given Rotations","[{\"question\":\"What rotation formulas are used to find the new coordinates?\",\"answer\":\"The document uses x1 = x·cos(θ) − y·sin(θ) and y1 = x·sin(θ) + y·cos(θ). These convert an original point (x, y) into a rotated point (x1, y1).\"},{\"question\":\"How does the example rotate the point (1,4) by 60°?\",\"answer\":\"It substitutes θ = 60° into the formulas to compute x1 and y1. The resulting location is shown as approximately (-2.98, 2.87).\"},{\"question\":\"What kinds of rotation problems are included in the answer key?\",\"answer\":\"The answer key lists multiple items asking to rotate shapes by specific angles (such as 157°, 182°, 172°, and 303°) around a reference point, including the origin (0,0).\"}]","Rotating Around Axis - Answer Key - Rotate Each Shape with New Coordinates | PDF",1790773014]