Line given:
  y = m*x + y_0

Point given:
  (a,b)

Miscellany:
  n = -1/m (perpendicular slope)

Point reflected over line:
  (c,d)

Newfangled constant of death:
  Death = (y_0 - b + n*a)/(n - m)

Then,
  c = 2*Death - a
  d = 2(m*Death + y_0) - b