Question

Where should the cell phone tower be located?

Answer 1

The tower should be put in the centroid of the triangle, since it is the points with equal distance from all the vertices.

The formula for the centroid is

$C = \left( \frac{x_A+x_b+x_C}{3}, \frac{y_A+y_b+y_C}{3} \right)$

i.e., you compute the arithmetic mean of the coordinates of the vertices. In your case:

$C = \left( \frac{1+13+13}{3}, \frac{1+6+1}{3} \right) = \left( \frac{27}{3}, \frac{8}{3} \right) = \left( 9, \frac{8}{3} \right)$