Rotation in the Cartesian Plane about the Origin

1. A rotation through ± 180° about (0,0) gives the same image P*
2. A rotation through ± 360° or 0° about (0,0) does not change the position.
   of the object.

The following table shows the image of the point (a, b) through the indicated angle of rotation about the origin

Rotation in the Cartesian Plane about a point (x,y)

In general, a point (a, b) rotated through 180* about (x, y) is mapped onto the point (2x - a, 2y - b).

Following the same pattern, the image of a point (a, b) rotated about (1,4) through 180° is

(2 x 1 - a, 2 x 4 - b).