Question

Find the equation of the perpendicular bisector of the segment with the endpoints of (-3, 4) and (1, -2).

Answer 1

find the equation in slope- intercept form

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

We require to find the slope and the midpoint of the given line segment

Find the slope using the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (- 3, 4 ) and (x₂, y₂ ) = (1, - 2 )

m =
`(-2-4)/(1+3)` =
`(-6)/(4)` = -
`(3)/(2)`

the slope of the perpendicular is the negative inverse of m

`m_(perpendicular)` =
`(2)/(3)`

Find the midpoint using the midpoint formula

midpoint = [
`(1)/(2)`(- 3 + 1),
`(1)/(2)`(4 - 2)] = (- 1, 1)

y =
`(2)/(3)` x + c ← is the partial equation

To find c substitute (- 1, 1 ) into the partial equation

1 = -
`(2)/(3)` + c ⇒ c =
`(8)/(3)`

y =
`(2)/(3)` x +
`(8)/(3)` ← equation of perpendicular bisector