The core elements of performance required by this task are:[br]Geometry High School[br]Congruence G-CO[br]Experiment with transformations in the plane[br]4. Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.[br][br]Similarity, Right Triangles, and Trigonometry G-SRT[br]Understand similarity in terms of similarity transformations[br]1. Verify experimentally the properties of dilations given by a center and a scale factor:[br]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. [br]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 [math]\Delta[/math]ABC to the image [math]\Delta[/math]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 [i]Always True, Sometimes True, or Never True.[br][br][/i]Complete Kay's chart, writing in each empty cell whether the transformation is [b]Always True, Sometimes True, or Never True.[/b]
Explain the reason for your answer to the orientation under rigid motions.
Klay drew the pre-image [math]\Delta[/math]XYZ. He wants to draw a dilation whose center is (1,2) and has a scale factor of [math]\frac{1}{2}[/math].
Draw the image [math]\Delta[/math]X'Y'Z' on the grid above under the dilation whose center is (1,2) and has a scale factor of [math]\frac{1}{2}[/math]. Show the image and center of the dilation.