Question

Find an equation for the perpendicular bisector of the line segment whose endpoints are (7,1)(7,1) and (-9,9)(−9,9)

Answer 1

First we are going to find the slope of these two endpoints.

Slope =
`(Y2-Y1)/(X2-X1)`

Slope =
`(9-1)/(-9-7)`
Slope =
`(8)/(-16)`
Slope =
`- (1)/(2)`

Because we need the perpendicular bisector, we do the opposite reciprocal of the slope. This is positive two.

Your perpendicular equation begins as y = 2x + b

To find where it will bisect, we need to find the midpoint of the two endpoints.

Midpoint =
`( (X1+X2)/(2) , (Y1+Y2)/(2) )`

Mdpt =
`( (7+(-9))/(2) , (1+9)/(2) )`
Mdpt =
`( (-2)/(2) , (10)/(2) )`
Mdpt = (- 1, 5)

We plug this into our incomplete equation to solve for b.

5 = 2(- 1) + b
5 = - 2 + b
7 = b

Your perpendicular bisector equation is y = 2x + 7