Question

Find an equation for the perpendicular bisector of the line segment whose endpoints are ( − 1 , − 1 ) (−1,−1) and ( 9 , 7 ) (9,7)

Answer 1

y = -
`(5)/(4)` x + 8

Explanation:

The perpendicular bisector intersects the line segment at its midpoint and is perpendicular to it.

Using the midpoint formula

M = (
`\frac{x_{}+x_(2) }{2}`,
`(y_(1)+y_(2) )/(2)` )

with (x₁, y₁ ) = (- 1, - 1) and (x₂, y₂ ) = (9, 7)

midpoint = (
`(-1+9)/(2)`,
`(-1+7)/(2)` ) = (
`(8)/(2)`,
`(6)/(2)` ) = (4, 3 )

Calculate the slope using the slope formula

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

with (x₁, y₁ ) = (- 1, - 1) and (x₂, y₂ ) = (9, 7)

m =
`(7-(-1))/(9-(-1))` =
`(7+1)/(9+1)` =
`(8)/(10)` =
`(4)/(5)`

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

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/((4)/(5) )` = -
`(5)/(4)` , then

y = -
`(5)/(4)` x + c ← is the partial equation

To find c substitute (4, 3) into the partial equation

3 = - 5 + c ⇒ c = 3 + 5 = 8

y = -
`(5)/(4)` x + 8 ← equation of perpendicular bisector

Answer 2

Place the compass at one end of line segment.

Adjust the compass to slightly longer than half the line segment length.

Draw arcs above and below the line.

Keeping the same compass width, draw arcs from other end of line.

Place ruler where the arcs cross, and draw the line segment.