17. A hospital trauma center is going to be built equidistant from three cities. Positioned on a grid, the cities would be located at (1, 5), (2, -2), and (-6, -2). What are the coordinates of the location where the trauma center should be built? A (-2, -1) C (2, -1) B (-2, 1) D (2.1)​

9514 1404 393

  B (-2, 1)

Step-by-step explanation:

The trauma center will be located at the circumcenter of the triangle. That is the point of intersection of the perpendicular bisectors of the sides. Once the points are graphed, it is pretty easy to see where that will be. It is on the line x=-2, above the x-axis. Only one answer choice is appropriate:

  (-2, 1)

_____

Line AC has a slope of 1. Those points are separated by 7 units horizontally and vertically, so the midpoint is 3.5 units horizontally and vertically from either point, at (-2.5, 1.5). The perpendicular line with slope -1 through that point will intersect x=2 at y=1.