http://www.ck12.org Chapter 3. Parallel and Perpendicular Lines
3.6 The Distance Formula
Learning Objectives
- Find the distance between two points.
- Find the shortest distance between a point and a line and two parallel lines.
- Determine the equation of a perpendicular bisector of a line segment in the coordinate plane.
Review Queue
- What is the equation of the line between (-1, 3) and (2, -9)?
- Find the equation of the line that is perpendicular toy=− 2 x+5 through the point (-4, -5).
- Find the equation of the line that is parallel toy=^23 x−7 through the point (3, 8).
Know What?The shortest distance between two points is a straight line. To the right is an example of how far apart
cities are in the greater Los Angeles area. There are always several ways to get somewhere in Los Angeles. Here,
we have the distances between Los Angeles and Orange. Which distance is the shortest? Which is the longest?
The Distance Formula
The distance between two points(x 1 ,y 1 )and(x 2 ,y 2 )can be defined asd=
√
(x 2 −x 1 )^2 +(y 2 −y 1 )^2. This formula
will be derived in Chapter 9.
Example 1:Find the distance between (4, -2) and (-10, 3).
Solution:Plug in (4, -2) for(x 1 ,y 1 )and (-10, 3) for(x 2 ,y 2 )and simplify.