Rotation With Variable Angle
Here is an example where you can vary the angle of rotation. The original figure is rotated counterclockwise about the center of rotation F by the angle Beta shown on the slider at the bottom of the screen. You can change Beta by increments of 5 degrees at a time to see what happens to the image under this rotation (just click left or right on the slider, or click and drag Beta to watch what happens).
You can also move F and/or move vertices of the original figure. Have fun playing!