Question

P (5,) and Q (-1, 2) are points on a straight line. Find the equation of the perpendicular bisector of PQ: y = mx+c
how to find missing

Answer 1

If the y-coordinate of P is missing, you need to supply it.

If it is not given, then use w to complete the problem.
P(5,w),Q(-1,2),
Mid-point: M((5-1)/2, (w+2)/2)=(Mx,My)
Slope of PQ:
m=(2-w)/(-1-5)
slope of perpendicular:
m'=-(-1-5)/(2-w)=6/(2-w)

Perpendicular bisector must pass through M, use the Point-slope form:
(y-y1)=m(x-x1)
so
y-My = (6/(2-w)) (x-Mx)