Points Equidistant from Point and Line
Date: 08/30/2001 at 08:13:33 From: Arun Yegneswaran Subject: Locus My teacher has given me the task of finding the locus of points that are equidistant from a point and a line. I have to plot as many of these points as possible on a sheet of paper and join them to get the locus. Can you please help me?
Date: 08/30/2001 at 12:47:33 From: Doctor Peterson Subject: Re: Locus Hi, Arun. You will eventually learn the name and formula for this important curve, but for now you only have to plot some points on it. Draw a line and a point not on the line. Now choose a distance. Set a compass for that distance, and draw a circle with that radius around the point; this will give all points the chosen distance away from the point. Now construct a line parallel to the given line, at the chosen distance. This gives all points that are that distance from the line. (Actually, you would need two parallel lines to make my last sentence true; can you see why one of the two lines is enough?) The line and circle you have drawn will, if the distance is great enough, intersect in two points. At those points, the distance from the point is the same as the distance from the line, so they are part of the locus. Repeat this for different distances, and you will have plotted the locus, two points at a time. You can probably find a way to do this faster; for instance, make a set of parallel lines spaced an inch apart, and then draw the circles that match them. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
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