3.6. The Distance Formula http://www.ck12.org
d=√
( 3 − 1 )^2 +(− 1 − 5 )^2
=
√
( 2 )^2 +(− 6 )^2
=
√
2 + 36
=
√
38 ≈ 6. 16 unitsShortest Distance between Two Parallel Lines
The shortest distance between two parallel lines is the length of the perpendicular segment between them. It doesn’t
matter which perpendicular line you choose, as long as the two points are on the lines. Recall that there are infinitely
many perpendicular lines between two parallel lines.
Notice that all of the pink segments are the same length. So, when picking a perpendicular segment, be sure to pick
one with endpoints that are integers.
Example 3:Find the distance betweenx=3 andx=−5.
Solution:Any line withx=anumber is a vertical line. In this case, we can just count the squares between the two
lines. The two lines are 3−(− 5 )units apart, or 8 units.
You can use this same method with horizontal lines as well. For example,y=−1 andy=3 are 3−(− 1 )units, or 4
units apart.
Example 4:What is the shortest distance betweeny= 2 x+4 andy= 2 x−1?