Question

A line segment has endpoints at (4, –6) and (0, 2). What is the slope of the given line segment? What is the midpoint of the given line segment? What is the slope of the perpendicular bisector of the given line segment? What is the equation, in slope-intercept form, of the perpendicular bisector?

Answer 1

-2

(2,-2)

1/2

y=(1/2)x-3

Explanation:

It’s correct on edge.

Answer 2

slope = - 2, midpoint = (2, - 2 )

the slope m is calculated using the ' gradient formula '

m = ( y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (4, - 6 ) and (x₂, y₂ ) = (0, 2 )

m =
`(2+6)/(0-4)` =
`(8)/(-4)` = - 2

calculate midpoint using midpoint formula

{
`(1)/(2)` (4 + 0 ),
`(1)/(2)` (- 6 + 2 )] = (2, - 2 )

gradient of perpendicular bisector = -
`(1)/(-2)` =
`(1)/(2)`

equation in slope-intercept form is

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

partial equation is y =
`(1)/(2)` x + c

to find c substitute ( 2, - 2) into the partial equation

- 2 = 1 + c ⇒ c = - 3

y =
`(1)/(2)` x - 3 in slope-intercept form