what is the equation for the perpendicular bisector of the line segment whose endpoints are (-7,2) (-1,-6)

Answer 1

The formula is y-y1= m*(x-x1)

1. Find the midpoint= [(x1-x2)/2, (y1-y2)/2]
you will get (-4,-2)

2. Find slope m1= [2-(-6)]/[-7-(-1)]= 8/-6=-4/3

3. find the slope of the perpendicular line
m1*m2=-1
-4/3*m2= -1
m2= 3/4

4. Plug in given points (-7,2) and (-1,-6) and m2 in the formula that I wrote in the beginning

y-(-2)=3/4(x-(-4))
y+2=3/4(x+4)
y+2=3/4x+3
y=3/4x+1 this is the equation your were looking for.

Please, make sure the numbers are correct and double check the math (in case of typo), but the actual idea is correct.

Answer 2

Indicate the equation of the line that is the perpendicular bisector of the segment with endpoints (4, 1) and (2, -5).