Understands and applies transformations
Transformations, such as reflections and rotations, are mappings that move points. For example, a 90-degree rotation is a transformation that rotates all points 90 degrees about a center of rotation. A reflection in the x-axis flips all points over the x-axis.
Students should be familiar with three classes of transformations: (1) transformations that preserve distance (called isometries or rigid motions, such as reflections, rotations, translations), (2) transformations that preserve shape (such as size transformations, dilations, or similarity transformations), and (3) transformations that change distance and shape (e.g., shears). Students should recognize similarity and congruence in terms of certain transformations.
Students should be able to identify, create, describe, and justify transformations using multiple representations. They should be able to find and describe an image under a given transformation and/or composition of transformations. Students should also be able to identify the transformations that produced a given image. Transformations should be represented algebraically (using coordinate rules, matrices, vectors, equations), and those representations should be used to analyze and reason about transformations.