   SEARCH HOME Math Central Quandaries & Queries  Question from Kristie, a student: I can't figure out how to determine the distance between parallel lines I am taking linear algebra and vector geometry. I was given two lines in the form #x+#y =# told they were parallel and asked to find the distance between them?? Please help Thanks Hi Kristie,

I don't know what you have learned in your class so I may not be showing you the most efficient way to solve this problem but I can show you an elementary method, that is a method that doesn't use vectors or anything special about linear algebra.

The lines are in the XY-plane so you can write the two equations in the form y = mx + b and y = mx + c. Notice that the two lines have the same slope m they are parallel. The point (0, b) is on the first line and hence the line through this point with slope -1/m is perpendicular to the first line. Find the point (p, q) where this line intersects the second line and then find the distance between (0, b) and (p, q).

Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.