Question

What's the equation of the line that's a perpendicular bisector of the segment
connecting A(-2, 8) and B(-4, 2)?

Answer 1

Answer: What's the equation of the line that's a perpendicular bisector of the segment connecting A (–2, 8) and B (–4, 2)? Question 12 options:

Step-by-step explanation:

Answer 2

Answer:

y = - $\frac{1}{3}$ x + 4

Step-by-step explanation:

The perpendicular bisector bisects AB at right angles

The midpoint of AB using the midpoint formula

$M_{AB}$ = ( $\frac{x_{1+x_{2} } }{2}$ , $\frac{y_{1}+y_{2} }{2}$ )

with (x₁,y₁ ) = A (- 2, 8 ) and (x₂, y₂ ) = B (- 4, 2 )

$M_{AB}$ = ( $\frac{-2-4}{2}$ , $\frac{8+2}{2}$ ) = ( $\frac{-6}{2}$ , $\frac{10}{2}$ ) = (- 3, 5 )

Calculate the slope m of AB using the slope formula

m = $\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$ = $\frac{2-8}{-4-(-2)}$ = $\frac{-6}{-4+2}$ = $\frac{-6}{-2}$ = 3

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

$m_{perpendicular}$ = - $\frac{1}{m}$ = - $\frac{1}{3}$

The perpendicular bisector passes through (- 3, 5 ) with slope = - $\frac{1}{3}$

The equation in slope- intercept form is

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

y = - $\frac{1}{3}$ x + c ← is the partial equation

To find c substitute (- 3, 5 ) into the partial equation

5 = 1 + c ⇒ c = 5 - 1 = 4

y = - $\frac{1}{3}$ x + 4 ← equation of perpendicular bisector