Question

Find an equation for the perpendicular bisector of the line segment connecting the points (-2, 5) and (3, -7).

Answer 1

the slope of the line between these points is
(-7-5)/(3+2) = -12/5

so the slope of our bisector = -1/(-12/5)
= 5/12

so our perpendicular bisector is of form
y = (5/12) x + b

now it has to go through a point halfway between the given ones
average x = (-2+3)/2
average y = (5-7)/2
so (1/2 , -1 )
put that in our equation to find b
-1 = (5/12)(1/2) + b
-1 = 5/24 + b
b = -29/24
so
y = (5/12) x -29/24
y = (10/24)x - 29/24
24 y = 10 x - 29