If algebraic sum of distances of a variable line from points (2, 0), (0, 2) and (– 2, – 2) is zero, then the line passes through the fixed point

Let the equation of the variable line beax+by+c=0then according to the given condition2a+ca2+b2+2b+ca2+b2+−2a−2b+ca2+b2=0⇒ c=0which shows that the line passes through (0, 0) for all values of a and b.