Posted by Joel on October 27, 2002 at 18:31:33:
In Reply to: right triangles posted by Jerry on October 27, 2002 at 13:12:52:
: Find all possible values of k so that (3,5), (5,-1), and (k,8)
: are the vertices of a right triangle.
: I start off getting an hypotenuse = 2sqrt(10) with sides 2 and 6, using (3,5) and (5,-1).
: Looking for an easier way.
Line segment through (3,5) and (5,-1) has slope:
(-1-5)/(5-3) = -3
You are looking for two lines that are perpendicular to that one; one passing through the point (3,5), and the other passing through the point (5,-1). The slope of both of those lines will be 1/3.
You know the slope and you know one point for each of those lines, so you can easily find their equations. Then solve those equations for y=8.
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