{"id":9205,"date":"2020-12-04T12:51:29","date_gmt":"2020-12-04T07:21:29","guid":{"rendered":"https:\/\/www.aplustopper.com\/?p=9205"},"modified":"2020-12-04T16:54:31","modified_gmt":"2020-12-04T11:24:31","slug":"general-transformation-vocabulary","status":"publish","type":"post","link":"https:\/\/www.aplustopper.com\/general-transformation-vocabulary\/","title":{"rendered":"General “Transformation” Vocabulary"},"content":{"rendered":"
The following vocabulary terms will appear throughout the lessons in the section on Transformational Geometry<\/strong>.<\/p>\n Image:<\/strong> An image is the resulting point or set of points under a transformation. For example, if the reflection of point P in line l is P’, then P’ is called the image of point P under the reflection. Such a transformation is denoted rl<\/sub> (P) = P’. Isometry:<\/strong> An isometry is a transformation of the plane that preserves length. For example, if the sides of an original pre-image triangle measure 3, 4, and 5, and the sides of its image after a transformation measure 3, 4, and 5, the transformation preserved length. Invariant:<\/strong> A figure or property that remains unchanged under a transformation of the plane is referred to as invariant. No variations have occurred.<\/p>\n Opposite Transformation:<\/strong> An opposite transformation is a transformation that changes the orientation of a figure. Reflections and glide reflections are opposite Orientation:<\/strong> Orientation refers to the arrangement of points, relative to one another, after a transformation has occurred. For example, the reference made to the direction traversed (clockwise or counterclockwise) when traveling around a geometric figure. Position vector:<\/strong> A position vector is a coordinate vector whose initial point is the origin. Any vector can be expressed as an equivalent position vector by translating the vector so that it originates at the origin.<\/p>\n Transformation:<\/strong> A transformation of the plane is a one-to-one mapping of points in the plane to points in the plane.<\/p>\n Transformational Geometry:<\/strong> Transformational Geometry is a method for studying geometry that illustrates congruence and similarity by the use of transformations.<\/p>\n Transformational Proof:<\/strong> A transformational proof is a proof that employs the use of transformations.<\/p>\n Vector:<\/strong> A quantity that has both magnitude and direction; represented geometrically by a directed line segment.<\/p>\n","protected":false},"excerpt":{"rendered":" General “Transformation” Vocabulary The following vocabulary terms will appear throughout the lessons in the section on Transformational Geometry. Image: An image is the resulting point or set of points under a transformation. For example, if the reflection of point P in line l is P’, then P’ is called the image of point P under […]<\/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":[3364,3363,3365,3366,3367,3362,3368,3369,3370],"yoast_head":"\n
\n<\/p>\n
\nA direct isometry preserves orientation or order – the letters on the diagram go in the same clockwise or counterclockwise direction on the figure and its image.
\nA non-direct or opposite isometry changes the order (such as clockwise changes to counterclockwise).
\n<\/p>\n
\ntransformations.
\nFor example, the original image, triangle ABC, has a clockwise orientation – the letters A, B and C are read in a clockwise direction. After the reflection in the x-axis, the image triangle A’B’C’ has a counterclockwise orientation – the letters A’, B’, and C’ are read in a counterclockwise direction.
\nA reflection is an opposite transformation.<\/p>\n
\n(Also see the diagram shown under “Opposite Transformations”.)
\n<\/p>\n