[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-467567-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-467567-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-rotate-each-shape-answer-key","Rotating Around Axis - Rotate each shape - answer key","","Worksheets and an answer key focused on rotating geometric shapes about points in the coordinate plane. It presents the rotation angle notation (theta), the rotation formula for converting (x, y) to (x1, y1) using cosine and sine, and applies the method to find new coordinates after specific rotations. Example calculations are shown for a 60° rotation from an initial coordinate pair, followed by multiple practice problems using angles like 230°, 149°, 184°, and 216°.",{"@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-rotate-each-shape-answer-key/467567/",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-each-shape-answer-key/467567.png","ImageObject",300,407,{"name":42,"@type":43},"Asher","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-11-03","2026-09-30",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",7,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"What is the rotation formula for finding new coordinates after rotating by theta?","Question",{"text":63,"@type":64},"Use x1 = x×cos(θ) - y×sin(θ) and y1 = x×sin(θ) + y×cos(θ). Substitute the original x and y along with the rotation angle θ.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"How do you find the coordinates after rotating a shape 60° when it starts at (1,4)?",{"text":68,"@type":64},"Compute x1 = 1×cos(60) - 4×sin(60) and y1 = 1×sin(60) + 4×cos(60). The worksheet’s result is approximately (-2.98, 2.87).",{"name":70,"@type":61,"acceptedAnswer":71},"What angles and rotation points are used in the practice problems?",{"text":72,"@type":64},"The practice items include rotations such as 230° and 184° around specified points, and rotations like 149° and 216° around the point (0,0). The answer key provides the resulting coordinates for each item.","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},467567,1792926023,{"code":4,"msg":82,"data":83},"success",[84,88,92,95,100,105,109,114,119,122,126],{"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":96,"doc_module":4,"doc_module_name":25,"category_name":97,"show_sort_weight":98,"slug":99},5,"Comic",60,"comic",{"id":101,"doc_module":4,"doc_module_name":25,"category_name":102,"show_sort_weight":103,"slug":104},6,"Technology",50,"technology",{"id":55,"doc_module":4,"doc_module_name":25,"category_name":106,"show_sort_weight":107,"slug":108},"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":96,"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:  \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-230° around the point 2) Rotate the shape 149° around the point (0,0) . (0,0) .  \n3) Rotate the shape-184° around the point 4) Rotate the shape 216° around the point (0,0) . (0,0) .  \n[Math](Math www.CommonCoreSheets.com 3 1-4)[ www.CommonCoreSheets.com](Math www.CommonCoreSheets.com 3 1-4)[ 3](Math www.CommonCoreSheets.com 3 1-4)[ 1-4](Math www.CommonCoreSheets.com 3 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>\u003Cbr>1) Rotate the shape-230° around the point 2) Rotate the shape 149° around the point (0,0) . (0,0) . | Answers 1.  (-1,-4.3) \u003Cbr>2.  (0.2,3.6)  3.  (-3.6,-6.3)  4.  (7.8,0.5)  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- |\n| (4 - 2) ,\u003Cbr>II I\u003Cbr>III IV\u003Cbr>\u003Cbr>\u003Cbr>(- 2, 3)\u003Cbr>II I\u003Cbr>III IV\u003Cbr>\u003Cbr>|  |  |  |  |  |\n| 3) Rotate the shape-184° around the point 4) Rotate the shape 216° around the point (0,0) . (0,0) . |  |  |  |  |  |\n| (4 - 6) , I \u003Cbr>II I\u003Cbr>II IV\u003Cbr>\u003Cbr>\u003Cbr>(- 6, 5) I\u003Cbr>II I\u003Cbr>II IV\u003Cbr>\u003Cbr>|  |  |  |  |  |\n|  |  |  |  |  |  |\n\n[Math](Math www.CommonCoreSheets.com 3 1-4)[ www.CommonCoreSheets.com](Math www.CommonCoreSheets.com 3 1-4)[ 3](Math www.CommonCoreSheets.com 3 1-4)[ 1-4](Math www.CommonCoreSheets.com 3 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>\u003Cbr>1) Rotate the shape-230° around the point 2) Rotate the shape 149° around the point (0,0) . (0,0) .\u003Cbr>\u003Cbr>II I\u003Cbr>III IV\u003Cbr>\u003Cbr>\u003Cbr>II I\u003Cbr>III IV\u003Cbr>| Answers\u003Cbr>1.  \u003Cbr>2.   |\n| --- | --- |\n\nMath  \nModified  \n[www.CommonCoreSheets.com](www.CommonCoreSheets.com)  \n3  \n1-2 50 0  \n\n|  |  |\n| --- | --- |","cbCaigopDiTOVgV7","https://ap.wps.com/l/cbCaigopDiTOVgV7","pdf",55454,"English","# Rotate each shape\n## Rotation formula\n## Worked example (60°)\n## Practice rotations and final answers","[{\"question\":\"What is the rotation formula for finding new coordinates after rotating by theta?\",\"answer\":\"Use x1 = x×cos(θ) - y×sin(θ) and y1 = x×sin(θ) + y×cos(θ). Substitute the original x and y along with the rotation angle θ.\"},{\"question\":\"How do you find the coordinates after rotating a shape 60° when it starts at (1,4)?\",\"answer\":\"Compute x1 = 1×cos(60) - 4×sin(60) and y1 = 1×sin(60) + 4×cos(60). The worksheet’s result is approximately (-2.98, 2.87).\"},{\"question\":\"What angles and rotation points are used in the practice problems?\",\"answer\":\"The practice items include rotations such as 230° and 184° around specified points, and rotations like 149° and 216° around the point (0,0). The answer key provides the resulting coordinates for each item.\"}]","Rotating Around Axis - Rotate each shape - answer key | PDF",1790773014]