Pentagon Rotation on Coordinate Grid

What are the coordinates of the other points for the figure? How do the coordinates change when you rotate the figure to 180, 270, or 360 degrees?

Rotation of a Point

The slider alpha controls the angle of rotation around the origin O. Change the angle of rotation and see Point A' change. You may also move Point A with the mouse.

Can you determine the coordinates of Point A' if you were given the value of the slider alpha and the coordinates of Point A? Come up with a conjecture and test it for different values of slider alpha and positions of Point A.