To perform a 90° rotation clockwise around the origin, you take the coordinates of the point A(x, y) and transform them to A'(y, -x). Since 180° and 270° are both "steps" of 90°, we can do this in succession and achieve our goal.
1) (5, 2) 90° = (2, -5) [(y, -x)]
2) (5, 2) 180° = two 90° turns = (2, -5) rotated 90° = (-5, -2)
3) (5, 2) 270° = three 90° turns = (-5, -2) rotated 90° = (-2, 5)°
4) (-5, 2) 90° = (y, -x) = (2, 5)
5) (-5, 2) 180° = two 90° turns = (2, 5) rotated 90° = (5, -2)
6) (-5, 2) 270° = three 90° turns = (5, -2) rotated 90° = (-2, -5)
7) (-2, 5) 90° = (y, -x) = (5, 2)
8) (5, -2) 180° = (y, -x) with another 90° turn = (-2, -5) rotated 90° = (-5, 2)
