[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-274729-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-274729-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","transformations-cheat-sheet-reflections-translations-dilations-rotations","Transformations Cheat Sheet - Reflections, Translations, Dilations, Rotations","","Concise cheat sheet for geometric transformations in a coordinate plane, defining reflections, translations, dilations, and rotations with core properties such as whether each transformation is isometric and whether it preserves orientation. Includes coordinate-plane rules for common reflection axes (x-axis, y-axis, y=x, and through the origin), translation shifts by (h,k), dilation scaling from the origin and from non-origin points, and rotation mappings for standard angles in clockwise and counter-clockwise directions.",{"@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/transformations-cheat-sheet-reflections-translations-dilations-rotations/274729/",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/transformations-cheat-sheet-reflections-translations-dilations-rotations/274729.png","ImageObject",300,407,{"name":42,"@type":43},"Kyle","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-11-03","2026-09-15",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",30,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"How do reflections change points on the coordinate plane?","Question",{"text":63,"@type":64},"Reflections swap coordinates based on the chosen line: over the x-axis (x,y)->(x,−y), over the y-axis (x,y)->(−x,y), over y=x (x,y)->(y,x), and through the origin (x,y)->(−x,−y).","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"How are translations represented using coordinate changes?",{"text":68,"@type":64},"Translations move points by horizontal and vertical shifts: (x,y)->(x±h,y±k), where h and k represent the amounts of left/right and up/down movement. Left implies h is negative and down implies k is negative.",{"name":70,"@type":61,"acceptedAnswer":71},"What coordinate rule applies to rotations by standard angles?",{"text":72,"@type":64},"For counter-clockwise 90°: (x,y)->(−y,x); for counter-clockwise 180°: (x,y)->(−x,−y); and for counter-clockwise 270°: (x,y)->(y,−x), with corresponding clockwise mappings also listed.","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},274729,1789482387,{"code":4,"msg":82,"data":83},"success",[84,88,92,95,100,105,110,114,119,122,126],{"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":106,"doc_module":4,"doc_module_name":25,"category_name":107,"show_sort_weight":108,"slug":109},7,"Healthcare",40,"healthcare",{"id":111,"doc_module":4,"doc_module_name":25,"category_name":112,"show_sort_weight":55,"slug":113},8,"Research & Report","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":22,"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":80,"read_time":30},3985741905716,"https://ap-avatar.wpscdn.com/davatar_994ba38a5ba835b3df7d355c54d3ed8d","REFLECTIONS:  \n􀀹 Reflections are a flip.  \n􀀹 The flip is performed over the “line of reflection.” Lines of symmetry are examples of lines of reflection.  \n􀀹 Reflections are isometric, but do not preserve orientation.  \nCoordinate plane rules: Over the x-axis: (x, y) 􀃆 (x,–y)  \nOver the y-axis: (x, y) 􀃆 (–x, y)  \nOver the line y = x: (x, y) 􀃆 (y, x)  \nThrough the origin: (x, y) 􀃆 (–x,–y)  \nTRANSLATIONS:  \n􀀹 Translations are a slide or shift.  \n􀀹 Translations can be achieved by performing two composite reflections over parallel lines.  \n􀀹 Translations are isometric, and preserve orientation.  \nCoordinate plane rules:  \n(x, y) 􀃆 (x ± h, y ± k) where h and k are the horizontal and vertical shifts.  \nNote: If movement is left, then h is negative. If movement is down, then k is negative.  \nDILATIONS:  \n􀀹 Dilations are an enlargement / shrinking.  \n􀀹 Dilations multiply the distance from the point of projection (point of dilation) by the scale factor.  \n􀀹 Dilations are not isometric, and preserve orientation only if the scale factor is positive.  \nCoordinate plane rules:  \nFrom the origin dilated by a factor of “c”: (x, y) 􀃆 (cx, cy)  \nFrom non-origin by factor of “c”: count slope from point to projection point, multiply by “c,” count from projection point.  \nROTATIONS:  \n􀀹 Rotations are a turn.  \n􀀹 Rotations can be achieved by performing two composite reflections over intersecting lines. The resulting rotation will be double the amount of the angle formed by the intersecting lines.  \n􀀹 Rotations are isometric, and do not preserve orientation unless the rotation is 360o or exhibit rotational symmetry back onto itself.  \n􀀹 Rotations of 180o are equivalent to a reflection through the origin.  \nCoordinate plane rules:  \nCounter-clockwise: Clockwise: Rule:  \n90o 270o (x, y) 􀃆 (–y, x)  \n180o 180o (x, y) 􀃆 (–x,–y)  \n270o 90o (x, y) 􀃆 (y,–x)","cbCainpkqttLUihr","https://ap.wps.com/l/cbCainpkqttLUihr","pdf",411816,"English","# Reflections\n## Translation (Slide/Shift)\n## Dilations (Scale)\n## Rotations (Turn)","[{\"question\":\"How do reflections change points on the coordinate plane?\",\"answer\":\"Reflections swap coordinates based on the chosen line: over the x-axis (x,y)-\\u003e(x,−y), over the y-axis (x,y)-\\u003e(−x,y), over y=x (x,y)-\\u003e(y,x), and through the origin (x,y)-\\u003e(−x,−y).\"},{\"question\":\"How are translations represented using coordinate changes?\",\"answer\":\"Translations move points by horizontal and vertical shifts: (x,y)-\\u003e(x±h,y±k), where h and k represent the amounts of left/right and up/down movement. Left implies h is negative and down implies k is negative.\"},{\"question\":\"What coordinate rule applies to rotations by standard angles?\",\"answer\":\"For counter-clockwise 90°: (x,y)-\\u003e(−y,x); for counter-clockwise 180°: (x,y)-\\u003e(−x,−y); and for counter-clockwise 270°: (x,y)-\\u003e(y,−x), with corresponding clockwise mappings also listed.\"}]","Transformations Cheat Sheet - Reflections, Translations, Dilations, Rotations | PDF"]