5. Points $A(-1,0)$ and $B(4,0)$ are the vertices of an isosceles triangle $ABC$ with base $\overline{AB}$. Determine the coordinates of vertex $C$ if the area of triangle $ABC$ is 15 square units.
5. Sketch:

![](https://cdn.mathpix.com/cropped/2024_05_30_4ffb1f624eaee9da51d7g-2.jpg?height=691&width=465&top_left_y=631&top_left_x=641)

The length of the base is 5 units.

Since the area of the triangle must be 15 square units, the length of the height to the base $\overline{A B}$ must be 6 units.

Given that $\triangle A B C$ is isosceles, the vertex $C$ is located on the perpendicular bisector of the base passing through the point $\mathrm{s}$ with coordinates $(1.5,0)$.

1 POINT

The problem has 2 solutions: $C_{1}(1.5,6)$ and $C_{2}(1.5,-6)$.

2 POINTS

Note: Correct answers without justification earn 3 points.