3.11. Distance Between Parallel Lines http://www.ck12.org
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.
Example B
What is the shortest distance betweeny= 2 x+4 andy= 2 x−1?
Graph the two lines and determine the perpendicular slope, which is−^12. Find a point ony= 2 x+4, let’s say (-1,
2). From here, use the slope of the perpendicular line to find the corresponding point ony= 2 x−1. If you move