The city councils of three neighboring towns-Ashton, Bradburg, and Carlville-decide to pool their resources and build a recreation center. To be fair, they decide to locate the recreation center equidistant from all three towns.
a. When a coordinate plane is placed on a map of the towns, Ashton is at (0, 4), Bradburg is at (3, 0), and Carlville is at (12, 8). At what point on the map should the recreation center be located?
b. If the three towns were collinear (along a line), could the recreation center be located equidistant from all three towns? Explain your reasoning.
c. What other factors might the three city councils consider while making their decision as to where to locate the recreation center?