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.
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.