http://www.ck12.org Chapter 3. Parallel and Perpendicular Lines
MEDIA
Click image to the left for more content.CK-12 Foundation: Chapter3DistanceBetweenParallelLinesB
Vocabulary
The√ distance formulatells us that 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.Guided Practice
- Find the distance betweenx=7 andx=−1.
- Find the distance betweeny=x+6 andy=x−2.
- Find the distance betweeny=5 andy=−6.
Answers:
- These are vertical lines, so we can just count the squares between the two lines. The two lines are 7−(− 1 )units
apart, or 8 units. - Find the perpendicular slope:m=1, som⊥=−1. Then, find they−intercept of the top line,y=x+6: (0, 6).
Use the slope and count down 1 and to the right 1 until you hity=x−2 at the point (4, 2). Use these two points in
the distance formula to determine how far apart the lines are.
d=√
( 0 − 4 )^2 +( 6 − 2 )^2
=
√
(− 4 )^2 +( 4 )^2
=
√
16 + 16
=
√
32 = 5. 66 units- These are horizontal lines, so we can just count the squares between the two lines. The two lines are 5−(− 6 )
units apart, or 11 units.
Practice
Use each graph below to determine how far apart each the parallel lines are. Round your answers to the nearest
hundredth.
1.
2.
3.
4.
Determine the shortest distance between the each pair of parallel lines. Round your answer to the nearest hundredth.