{"id":9295,"date":"2023-04-27T10:00:45","date_gmt":"2023-04-27T04:30:45","guid":{"rendered":"https:\/\/www.aplustopper.com\/?p=9295"},"modified":"2023-04-28T09:51:35","modified_gmt":"2023-04-28T04:21:35","slug":"translations","status":"publish","type":"post","link":"https:\/\/www.aplustopper.com\/translations\/","title":{"rendered":"Translations"},"content":{"rendered":"
A translation<\/strong> “slides” an object a fixed distance in a given direction. The original object and its translation have the same shape and size, and they face in the same direction. A translation creates a figure that is congruent with the original figure and preserves distance (length) and orientation (lettering order). A translation is a direct isometry<\/strong>. Definition:<\/strong> A translation (notation Ta,b<\/sub><\/strong>) is a transformation of the plane that slides every point of a figure the same distance in the same direction.<\/p>\n Ta,b<\/sub>(x, y) = (x+a, y+b)<\/strong><\/p>\n Translations in the Coordinate Plane: Translations A translation “slides” an object a fixed distance in a given direction. The original object and its translation have the same shape and size, and they face in the same direction. A translation creates a figure that is congruent with the original figure and preserves distance (length) and orientation (lettering order). A translation is […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[5],"tags":[3413],"yoast_head":"\n
\nProperties preserved (invariant) under a translation:<\/strong><\/p>\n\n
\n<\/li>\n
\nIn the example below, notice how each vertex moves the same distance in the same direction.
\nIn this next example, the “slide” (translation) moves the figure 7 units to the left and 3 units down.
\nThere are several ways to indicate that a translation is to occur:<\/p>\n\n
\n(This is read: “the x and y coordinates will be translated into x-7 and y-3”. Notice that adding a negative value (subtraction), moves the image left and\/or down, while adding a positive value moves the image right and\/or up.)<\/li>\n
\n(The -7 tells you to subtract 7 from all of your x-coordinates, while the -3 tells you to subtract 3 from all of your y-coordinates.)
\nThis may also be seen as T-7,-3<\/sub>(x,y) = (x -7,y – 3)<\/strong>.<\/li>\n
\n
\n(A vector, a directed line segment, may also be used to show the movement of a translation. See more about vectors and translations.)<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"