Mappings of the plane
• Represent transformations in the plane using various tools (transparencies, geometry software, etc.). • Describe transformations as functions that take points in the plane as inputs and given other points as outputs. • Compare transformations that preserve distance and angle and those that do not (translation vs. horizontal stretch).
Students construct (with both compass and straight-edge and technology, rather than the physical models and transparencies used in eighth grade) perpendicular lines, parallel lines, and regular polygons, and develop formal definitions of these objects. Students then develop more precise definitions for translations, rotations, and reflections, and use these to describe symmetries - single rigid transformations that carry objects to themselves. Careful attention is given to properties of figures that are preserved (for example, as the result of a translation, a line segment is both parallel and congruent to the pre-image), as they will be important to following work with transformational proofs. Additionally, coordinates are used to represent rigid motions as functions that map points in the plane to points in the plane.
Tasks
1
Horizontal Stretch of the Plane