Question

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

Answer 1

Answer:

y = 6x + 12

Step-by-step explanation:

We require the midpoint M and slope of AB

Using the midpoint formula, then

M = [ $\frac{1}{2}$ (3 - 9) , $\frac{1}{2}$ (- 7 - 5) ] = (- 3, - 6 )

Calculate the slope m using the slope formula

m = $\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

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

m = $\frac{-5+7}{-9-3}$ = $\frac{2}{-12}$ = - $\frac{1}{6}$

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

$m_{perpendicular}$ = - $\frac{1}{m}$ = - $\frac{1}{-\frac{1}{6} }$ = 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