http://www.ck12.org Chapter 3. Parallel and Perpendicular Lines
3.11 Distance Between Parallel Lines
Here you’ll learn that the shortest distance between two parallel lines is the length of a perpendicular line between
them.
What if you were given two parallel lines? How could you find how far apart these two lines are? After completing
this Concept, you’ll be able to find the distance between parallel lines using the distance formula.
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Click image to the left for more content.CK-12 Foundation: Chapter3DistanceBetweenParallelLinesA
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Click image to the left for more content.James Sousa:DeterminingtheDistance Between Two Parallel Lines
Guidance
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 A
Find the distance betweenx=3 andx=−5.
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.