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

1. ## 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.

2. 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, $\displaystyle (3, 4), (-2, 3)$ and $\displaystyle (x, y)$.

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

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

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# An equilateral triangle has two vertices at the point A(3,4) B(3,-3).Find the coordinate of vertex C

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