there are two points a(x1, y1) b(x2, y2), then the coordinates of their midpoint p are ((x1+x2)/2, (y1+y2)/2)

in addition: the symmetry point of any point (x, y) with respect to (a, b) is (2a-x, 2b-y), then (2a-x, 2b-y) is also on this function. there is f(2a-x)= 2b-y shift term, there is y=2b- f(2a-x)