The defining data of a rotation is a point O, called the center of rotation, and an angle ABC, called the angle of rotation.
If the point X is the center O, then the image X' is also O.
If the point X is not the center O, then the image X' is determined by the properties that OX = OX' and the measure of the angle XOX' equals the measure of the angle ABC.
Note: The measure of an angle is a real number mod 360.