# Given two vertices of triangle find co-ordinates of third.

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• July 2nd 2010, 11:44 PM
Ilsa
Given two vertices of triangle find co-ordinates of third.
An equilateral triangle has one vertex at the point (3,4) and another at the point (-2,3). Find the coordinates of the third vertex.
• July 2nd 2010, 11:50 PM
Prove It
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Originally Posted by Ilsa
An equilateral triangle has one vertex at the point (3,4) and another at the point (-2,3). Find the coordinates of the third vertex.

The triangle will have three points, $(3, 4), (-2, 3)$ and $(x, y)$.

Since it is an equilateral triangle, all the lengths are equal.

So use the distance formula to get the distance between $(3, 4)$ and $(-2, 3)$, then use the distance formula to find the other two distances, which will be functions of $x$ and $y$, and solve them simultaneously.