Finding the Other End of a Line Segment
Date: 07/25/2002 at 20:29:26 From: Dawn Langseth Subject: Finding a point I know a point location and I know the slope of the line. I also know the distance. How do I find the point at the other end of the line?
Date: 07/25/2002 at 23:11:04 From: Doctor Peterson Subject: Re: Finding a point Hi, Dawn. I would use vectors, though you don't need to know anything about them to do this. Suppose the slope is 3/4. Then one vector (directed segment) in this direction is (4,3) - 4 across and 3 up. If you draw a point 4 across and 3 up from the starting point, it will be in the right direction, but probably the wrong distance. So we find the length of our vector, sqrt(3^2 + 4^2) = sqrt(25) = 5, (which I chose to make the numbers easy), and divide by it. Our new vector, whose length will be 1, is (4/5,3/5). Now to get a vector of the desired length (say, 3) we can multiply by that and get (12/5,9/5). Just add that vector to your starting point (that is, add 12/5 to the x coordinate and 9/5 to y) and you have a point that is both in the right direction and at the right distance. Check the distance and see. I should mention that there are actually TWO points along the given line and at the right distance. I've chosen one direction; you can subtract my vector rather than adding it to get the other possibility. If you have any further questions, feel free to write back. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
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