Write an equation in point-slope form for the perpendicular bisector of the segment with endpoints A(-2,2) and B(5,4)

Question

Write an equation in point-slope form for the perpendicular bisector of the segment with endpoints A(-2,2) and B(5,4).

Answer 1

The perpendicular bisector of AB contains the midpoint, M, of AB.

M = ((-2+5)/2, (2+4)/2) = (1.5, 3)

The slope of the perpendicular bisector of AB is the negative reciprocal of the slope of AB.

So, since slope of AB = (4-2) / (5-(-2)) = 2/7, the perpendicular bisector has slope -7/2.

Equation of perpendicular bisector: y - 3 = (-7/2)(x - 1.5)

Simplify to get y = (-7/2)x + (33/4)