http://www.ck12.org Chapter 3. Parallel and Perpendicular Lines
d=√
( 0 − 3 )^2 +(− 3 − 6 )^2
=
√
(− 3 )^2 +(− 9 )^2
=
√
9 + 81
=
√
90 ≈ 9. 49 unitsPerpendicular Bisectors in the Coordinate Plane
Recall that the definition of a perpendicular bisector is a perpendicular line that goes through the midpoint of a line
segment. Using what we have learned in this chapter and the formula for a midpoint, we can find the equation of a
perpendicular bisector.
Example 6:Find the equation of the perpendicular bisector of the line segment between (-1, 8) and (5, 2).
Solution:First, find the midpoint of the line segment.
(
− 1 + 5
2
,
8 + 2
2
)
=
(
4
2
,
10
2
)
= ( 2 , 5 )
Second, find the slope between the two endpoints. This will help us figure out the perpendicular slope for the
perpendicular bisector.
m=2 − 8
5 + 1
=
− 6
6
=− 1
If the slope of the segment is -1, then the slope of the perpendicular bisector will be 1. The last thing to do is to
find they−intercept of the perpendicular bisector. We know it goes through the midpoint, (2, 5), of the segment, so
substitute that in forxandyin the slope-intercept equation.