3.6. The Distance Formula http://www.ck12.org
d=√
(− 1 + 3 )^2 +(− 3 + 2 )^2
=
√
22 +(− 1 )^2
=
√
4 + 1
=
√
5 ≈ 2. 24 unitsExample 5:Find the distance between the two parallel lines below.
Solution:First you need to find the slope of the two lines. Because they are parallel, they are the same slope, so if
you find the slope of one, you have the slope of both.
Start at they−intercept of the top line, 7. From there, you would go down 1 and over 3 to reach the line again.
Therefore the slope is−^13 and the perpendicular slope would be 3.
Next, find two points on the lines. Let’s use they−intercept of the bottom line, (0, -3). Then, rise 3 and go over 1
until your reach the second line. Doing this three times, you would hit the top line at (3, 6). Use these two points in
the distance formula to find how far apart the lines are.