Distance From a Point to a LineDate: 09/16/98 at 00:59:43 From: Marion Keehn Subject: Distance from a point to a line Dear Dr. Math, I'm trying to derive an equation that will give the distance from any point on a 2d plane to a line. I've been trying to make a line that crosses the original line and goes through the point with the negative inverse slope and the coordinates of the point. Then I'm using the Pythagorean formula to find the distance. I'm having trouble getting all the math right, so I was wondering if you might help me through it. Thanks, Marion Keehn Date: 09/16/98 at 01:52:29 From: Doctor Schwa Subject: Re: Distance from a point to a line I also have done this problem the way you suggest, and the algebra is rather messy. I eventually got the answer, but when I saw how simple it was, I knew there had to be a better way to get there. Probably an easier way to do this problem is to use similar triangles. If the original line is ax + by + c = 0, and the point we're looking at is (r, s), then the key triangle is the one you've identified (hypotenuse being a line parallel to the y-axis and down to touch the line, one leg being the perpendicular distance we want) and the other triangle is the one that shows the slope of the line. Putting those two together, and using similar triangles, I think you will find that the distance is |ar + bs + c| / sqrt(a^2 + b^2). If you need help finishing off the calculation, please write back. - Doctor Schwa, The Math Forum http://mathforum.org/dr.math/ |
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