Dilations Relations
The core elements of performance required by this task are:
Geometry High School
Congruence G-CO
Experiment with transformations in the plane
4. Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
Similarity, Right Triangles, and Trigonometry G-SRT
Understand similarity in terms of similarity transformations
1. Verify experimentally the properties of dilations given by a center and a scale factor:
a. A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.
b. The dilation of a line segment is longer or shorter in that ratio given by the scale factor.
Klay is exploring transformations, specifically dilations. He drew the following dilation of the pre-image of ABC to the image A'B'C'.
What point is the center of dilation?
What is the scale factor of the dilation?
Klay made a chart to compare rigid motion transformations with dilation transformations. In each cell Klay plans to write whether the "Under this transformation" the action is either Always True, Sometimes True, or Never True.
Complete Kay's chart, writing in each empty cell whether the transformation is Always True, Sometimes True, or Never True.
Explain the reason for your answer to the orientation under rigid motions.
Klay drew the pre-image XYZ. He wants to draw a dilation whose center is (1,2) and has a scale factor of .
Draw the image X'Y'Z' on the grid above under the dilation whose center is (1,2) and has a scale factor of . Show the image and center of the dilation.