Find an equation for the perpendicular bisector of the line segment whose endpoints are (-8,7) and (4,3)

First let’s find the gradient of the perpendicular bisector.

If the gradient of the line segment is m, then the gradient of its perpendicular bisector is -1/m.

Gradient of line= (y2-y1)/(x2-x1) =
(3-7)/(4- -8) = (-4/12) = -1/3

Therefore the gradient of the perpendicular bisector is 3

The perpendicular bisector will pass through the midpoint of line segment.

Midpoint of line= ((x1+x2)/2 , (y1+y2)/2)
=( (-8+4)/2 , (7+3)/2) = (-2,5)

Equation of perpendicular bisector : y=mx + c.

We know m is 3

So we have:

y=3x+c

The bisector passes through (-2,5). Replace in equation to find c.

5 = 3(-2) + c

5 = -6 + c
c = 5+6 = 11

So equation if bisector is y = 3x + 11