Question

Line segment AB has endpoints A(3, -7) and B(-9,-5). Find the equation of the perpendicular bisector

of AB.

Answer 1

y = 6x + 12

Explanation:

We require the midpoint M and slope of AB

Using the midpoint formula, then

M = [
`(1)/(2)` (3 - 9) ,
`(1)/(2)` (- 7 - 5) ] = (- 3, - 6 )

Calculate the slope m using the slope formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ ) = A(3, - 7) and (x₂, y₂ ) = B(- 9, - 5)

m =
`(-5+7)/(-9-3)` =
`(2)/(-12)` = -
`(1)/(6)`

Given a line with slope m then the slope of a line perpendicular to it is

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/(-(1)/(6) )` = 6

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = 6 , thus

y = 6x + c ← is the partial equation

To find c substitute M(- 3, - 6) into the partial equation

- 6 = - 18 + c ⇒ c = - 6 + 18 = 12

y = 6x + 12 ← equation of perpendicular bisector