Equation of Perpendicular Bisector

Question

What is the equation of the perpendicular bisector of the segment with endpoints (0,4) and (-4,2)?

Answer 1

The perpendicular bisector of a line segment must pass through its midpoint.

Midpoint = (-2, 3)

Slope of line segment = (2-4) / (-4-0) = 1/2

Slope of perpendicular bisector = -1 / (1/2) = -2

Equation of perpendicular bisector: y - 3 = -2(x + 2)

So, y = -2x - 1