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 lines.
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" <email@example.com> To: <firstname.lastname@example.org>; <email@example.com> 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?