Move around the points to investigate rotating an object around a center point.

Triangle ABC has vertices A(3, 2), B(9, 2), and C(4,5). P is the center of rotation.
1. Use the slider to rotate the preimage 90 degrees counterclockwise about the origin. Record the image points.
What do you notice about the angle formed by connecting the center of rotation to A and to A'? (Angle APA')
2. Move the center of rotation so that P is located at (1,2). How does this affect the location of the image triangle?
3. Move the center of rotation so that P is located at (3,2) so that the center of rotation is Vertex A. How does this affect the location of the image triangle?