A Right Triangle of Points
Date: 01/14/99 at 22:44:50 From: Matt Strenz Subject: Right triangle Determine the values of x that would make the points (x,0), (-2,1), and (3,4) the vertices of a right triangle. I have tried the problem but do not understand it. Could you give me some help please? Thank you.
Date: 01/15/99 at 13:02:12 From: Doctor Peterson Subject: Re: Right triangle Hi, Matt. I think I can point you in the right direction. The first thing I would do is to graph the points so we can see what we have: | C(3,4) 4+ * | 3+ | 2+ B(-2,1) | * 1+ | A(x,0) --+--+--+--+--+--+-- * -2 0 1 3 We have two points (B and C) nailed down, and one (A) that can slide anywhere along the x axis. We have to figure out what values of x will give us a right triangle. The trouble is, there are three ways we could get a right triangle, depending on which point is the right angle. So you really have three problems to solve. The easiest cases will be where one of the fixed points B or C is the right angle. You can find the slope of the segment BC, and from that you know what the slope of AB (or AC) has to be. (Remember that the slope of the perpendicular line is the negative reciprocal.) This will give you an equation like this to solve: 1 - 0 ------ = m -2 - x where m is the slope you calculated. If A is the right angle, you can make an equation based on the fact that AB and AC have to be perpendicular. That should give you a good start on the problem. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
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