-81-
Pre‐Algebra Introduction to Transformation A Transformation is a mapping of the pre‐image of a geometric figure onto an image that retains key characteristics of the pre‐image. Definitions The Pre‐Image is the geometric figure before it has been transformed. The Image is the geometric figure after it has been transformed. A mapping is an association between objects. Transformations are types of mappings. In the figures below, we say ABCD is mapped onto A’B’C’D’, or ’ ’ ’ ’. The order of the vertices is critical to a properly named mapping. An Isometry is a one‐to‐one mapping that preserves lengths. Transformations that are isometries (i.e., preserve length) are called rigid transformations. Isometric Transformations Reflection is flipping a figure across a line called a “mirror.” The figure retains its size and shape, but appears “backwards” after the reflection. Rotation is turning a figure around a point. Rotated figures retain their size and shape, but not their orientation. Translation is sliding a figure in the plane so that it changes location but retains its shape, size and orientation. Table of Characteristics of Isometric Transformations Transformation Reflection Rotation Translation Isometry (Retains Lengths)? Yes Yes Yes Retains Angles? Yes Yes Yes Retains Orientation to Axes? No No Yes Version 2.1
12/01/2010