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