First, we need to find the slope of the line:
Let:
(5, -4) = (x1,y1)
(-9, -8) = (x2,y2)
m = (y2-y1)/(x2-x1) = (-8-(-4))/(-9-5) = -4/-14 = 2/7
Also, we need to find the midpoint:
let:
MP = (xp,yp)
xp= (x1+x2)/2 = (5-9)/2 = -2
yp = (y1+y2)/2 = (-4-8)/2 = -6
MP = (-2, -6)
Now, the slope for the perpendicular bisector is -m = -7/2
y = -mx + b
Using the midpoint
-6 = -7/2(-2) + b
-6 = 7 + b
Solving for b:
b = -13
Therefore, the equation for the perpendicular bisector is:
y = -7x/2 - 13
