{"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":"

Translations<\/span><\/h2>\n

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>.
\n\"TranslationsProperties preserved (invariant) under a translation:<\/strong><\/p>\n

    \n
  1. distance (lengths of segments are the same)<\/li>\n
  2. angle measures (remain the same)
    \n\"Translations<\/li>\n
  3. parallelism (parallel lines remain parallel)<\/li>\n
  4. colinearity (points stay on the same lines)<\/li>\n
  5. midpoint (midpoints remain the same in each figure)<\/li>\n
  6. orientation (lettering order remains the same)<\/li>\n<\/ol>\n

    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:
    \nIn the example below, notice how each vertex moves the same distance in the same direction.
    \n\"TranslationsIn this next example, the “slide” (translation) moves the figure 7 units to the left and 3 units down.
    \n\"TranslationsThere are several ways to indicate that a translation is to occur:<\/p>\n

      \n
    1. Description:<\/strong> 7 units to the left and 3 units down. (A verbal description of the translation is given.)<\/li>\n
    2. Mapping:<\/strong> (x, y)\u2192(x-7, y-3)
      \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
    3. Notation:<\/strong>
      \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
    4. Vectors:<\/strong>
      \n\"Translations
      \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":"

      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":"\nTranslations - A Plus Topper<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.aplustopper.com\/translations\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Translations\" \/>\n<meta property=\"og:description\" content=\"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 […]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.aplustopper.com\/translations\/\" \/>\n<meta property=\"og:site_name\" content=\"A Plus Topper\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/aplustopper\/\" \/>\n<meta property=\"article:published_time\" content=\"2023-04-27T04:30:45+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2023-04-28T04:21:35+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/12\/Translations-1.jpg\" \/>\n<meta name=\"twitter:card\" content=\"summary\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"sastry\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Organization\",\"@id\":\"https:\/\/www.aplustopper.com\/#organization\",\"name\":\"Aplus Topper\",\"url\":\"https:\/\/www.aplustopper.com\/\",\"sameAs\":[\"https:\/\/www.facebook.com\/aplustopper\/\"],\"logo\":{\"@type\":\"ImageObject\",\"@id\":\"https:\/\/www.aplustopper.com\/#logo\",\"inLanguage\":\"en-US\",\"url\":\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/Aplus_380x90-logo.jpg\",\"contentUrl\":\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/Aplus_380x90-logo.jpg\",\"width\":1585,\"height\":375,\"caption\":\"Aplus Topper\"},\"image\":{\"@id\":\"https:\/\/www.aplustopper.com\/#logo\"}},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/www.aplustopper.com\/#website\",\"url\":\"https:\/\/www.aplustopper.com\/\",\"name\":\"A Plus Topper\",\"description\":\"Improve your Grades\",\"publisher\":{\"@id\":\"https:\/\/www.aplustopper.com\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/www.aplustopper.com\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"en-US\"},{\"@type\":\"ImageObject\",\"@id\":\"https:\/\/www.aplustopper.com\/translations\/#primaryimage\",\"inLanguage\":\"en-US\",\"url\":\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/12\/Translations-1.jpg\",\"contentUrl\":\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/12\/Translations-1.jpg\",\"width\":184,\"height\":191,\"caption\":\"Translations 1\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/www.aplustopper.com\/translations\/#webpage\",\"url\":\"https:\/\/www.aplustopper.com\/translations\/\",\"name\":\"Translations - 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