A new hospital is being planned to serve three towns: Farmington, Gladewater, and Hopedale. On a map, the coordinates of the towns are F(2,13), G(12,3), H(12,17), respectively. One proposal is to build the hospital at the point that is equidistant from the three towns.
a) Use analytic geometry methods to determine the coordinates of this point. (HINT: p. 126 #15)
b) Verify that this point is the same distance from each town.
c) List some reasons why this point might not be the best site for the new hospital.