Math CentralQuandaries & 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

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).


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