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Topic: finding third coordinate
Replies: 3   Last Post: Jun 11, 2009 9:21 AM

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Greg Pack

Posts: 1
Registered: 6/11/09
Re: finding third coordinate
Posted: Jun 11, 2009 9:21 AM
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Connect the points of the coordinates you are given and you have a segment
that is either a hypotenuse or a leg of your right triangle. Now all you
need is a third point. Easy. You can choose any point from one of three
infinite sets of possibilities. One set is a circle and the other two are

Suppose your segment is a hypotenuse. Find the midpoint and use it as the
center of a circle through the endpoints. Every point on this circle can be
the vertex of the right angle of your right triangle. Pick any point on the
circle [except the endpoints]. There are an infinite number of third points
you can use to find the coordinates. Use the standard equation of a circle
with your mid-point center (h, k) and a radius half the length of your
segment to show an equation for your locus of points.

Suppose your segment is a leg. Find the slope of your segment. Use the
opposite of the slope's reciprocal to give you the slope of a line
perpendicular to your leg. Now use the point-slope form of a linear
equation to find the equation of the line through each endpoint of your
[segment] leg. This line represents an infinite number of points that would
work as your third point to form a right triangle. Repeat the process and
you have another equation for another infinite set of possible third points.

Hope that helps.

----- Original Message -----
From: "koolelectrical" <smamalik24@gmail.com>
To: <geometry-pre-college@moderators.isc.org>;
Sent: Tuesday, June 09, 2009 6:43 AM
Subject: finding third coordinate

>I wanna know that how can i find third coordinate of right angled
> triangle when i know two coordinates?

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