CK-12 Geometry-Concepts

http://www.ck12.org Chapter 3. Parallel and Perpendicular Lines

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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

1. Find the distance betweenx=7 andx=−1.


2. Find the distance betweeny=x+6 andy=x−2.


3. Find the distance betweeny=5 andy=−6.

Answers:

1. 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.


2. 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

3. 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.