Properties of rotations

This is a time lapse photo of the night sky. Each streak in the photo shows one star moving across the night sky. Move point A to the start of any streak (where the star was located at the beginning of the time lapse photo). Notice that its image, A', always lands at the end of the streak. More importantly, A and A' are always equidistant from the center of rotation (point C); and the angle of rotation is always 10 degrees.