[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-467562-105":59,"doc-detail-467562-en":123},{"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":116,"head_meta":118,"extra_data":120,"updated_unix":122},105,"en","rotating-around-axis-rotation-worksheet","Rotating Around Axis - Rotation Worksheet","","Worksheets explain how to rotate points and shapes in the coordinate plane using an angle of rotation θ. The rotation rule is given with formulas x1 = x cos(θ) - y sin(θ) and y1 = x sin(θ) + y cos(θ). Worked examples compute new coordinates after rotating a point such as (1,4) by 60°, then tasks ask students to rotate shapes by different angles around (0,0). Answer key coordinates are provided for selected rotations.",{"@graph":69,"@context":115},[70,84,106],{"@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-rotation-worksheet/467562/",{"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-rotation-worksheet/467562.png","ImageObject",300,407,{"name":92,"@type":93},"Asher","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-03","2026-09-30",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",16,{"@type":107,"mainEntity":108},"FAQPage",[109],{"name":110,"@type":111,"acceptedAnswer":112},"What does it mean to rotate a shape around (0,0)?","Question",{"text":113,"@type":114},"Rotating around (0,0) means the origin is the center of rotation. The worksheet includes problems where the rotation angles are applied to each shape relative to that origin.","Answer","https://schema.org",{"og:url":83,"og:type":117,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":119,"canonical":83},"index,follow",{"doc_id":121,"site_id":62},467562,1790825933,{"code":4,"msg":5,"data":124},{"doc_id":121,"user_id":125,"nickname":92,"user_avatar":126,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":127,"file_id":128,"file_url":129,"file_type":130,"file_size":131,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":41,"language":132,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":133,"faqs":134,"seo_title":135,"seo_description":67,"update_tm":136,"read_time":137},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 231° around the point (0,0) .\u003Cbr>\u003Cbr>II I\u003Cbr>III IV\u003Cbr>| 2) Rotate the shape-205° around the point (0,0) .\u003Cbr>\u003Cbr>II I\u003Cbr>III IV\u003Cbr>|  |  |  |  |  |\n| 3) Rotate the shape-134° around the point 4) Rotate the shape-224° around the point (0,0) . (0,0) .\u003Cbr>\u003Cbr>\u003Cbr>II I\u003Cbr>III IV\u003Cbr>|  |  |  |  |  |  |\n|  |  |  |  |  |  |  |\n\n[Math](Math www.CommonCoreSheets.com 1 1-4)[ www.CommonCoreSheets.com](Math www.CommonCoreSheets.com 1 1-4)[ 1](Math www.CommonCoreSheets.com 1 1-4)[ 1-4](Math www.CommonCoreSheets.com 1 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.  (-6.6,-1.4) \u003Cbr>2.  (8.4,-3.8)  3.  (3,7)  4.  (5.7,-0.1)  |\n| --- | --- | --- |\n| 1) Rotate the shape 231° around the point (0,0) . | 2) Rotate the shape-205° around the point (0,0) .\u003Cbr>(- 6, -7 )\u003Cbr>II I\u003Cbr>III IV\u003Cbr>|  |\n| (3 - 6) ,\u003Cbr>II I\u003Cbr>III IV\u003Cbr>\u003Cbr>|  |  |\n| 3) Rotate the shape-134° around the point 4) Rotate the shape-224° around the point (0,0) . (0,0) . |  |  |\n| \u003Cbr>(- 4, -4 )\u003Cbr>II I\u003Cbr>III IV\u003Cbr>\u003Cbr>|  |  |\n\n[Math](Math www.CommonCoreSheets.com 1 1-4)[ www.CommonCoreSheets.com](Math www.CommonCoreSheets.com 1 1-4)[ 1](Math www.CommonCoreSheets.com 1 1-4)[ 1-4](Math www.CommonCoreSheets.com 1 1-4) 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 231° around the point (0,0) .\u003Cbr>\u003Cbr>II I\u003Cbr>III IV\u003Cbr>| 2) Rotate the shape-205° around the point (0,0) .\u003Cbr>\u003Cbr>II I\u003Cbr>III IV\u003Cbr>|  |\n\nMath  \nModified  \n[www.CommonCoreSheets.com](www.CommonCoreSheets.com)  \n1  \n1-2 50 0  \n\n|  |  |\n| --- | --- |\n\nRotating 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 th","cbCairKCgwPuVkK4","https://ap.wps.com/l/cbCairKCgwPuVkK4","pdf",565822,"English","# Rotate each shape\n## Rotation formula using θ\n## Sample rotation by 60°\n## Practice rotations around (0,0)\n## Answer key coordinates","[{\"question\":\"What does it mean to rotate a shape around (0,0)?\",\"answer\":\"Rotating around (0,0) means the origin is the center of rotation. The worksheet includes problems where the rotation angles are applied to each shape relative to that origin.\"}]","Rotating Around Axis - Rotation Worksheet | PDF",1790773005,76]