The image of P(a, b) on the line y = - x is Q and the image of Q on the line y = x is R. Then the midpoint of PR is
(a+b,b+a)
((a+b)/2,(b+2)/2)
(a−b,b−a)
(0,0)
The point Q is (-b, -a) and the point R is (-a, -b). Therefore, the midpoint of PR is (0, 0).