Find the midpoint (M) of AB, find the slope(m) of the line AB, then find the equation of the line through M with slope -1/m, which is the perpendicular bisector of AB.
Short way:
The perpendicular bisector of (x₁,y₁) and (x₂,y₂): 2(x₂-x₁)x + 2(y₂-y₁)y = x₂²-x₁²+y₂²-y₁².
Here this is 2(1-(-4))x + 2(6-4)y = 1²-(-4)²+6²-4² which is 10x + 4y = 5.
