In a rectangular coordinate system, points O (2,2), P (2,6), and Q (10,2) represent the sites of three proposed housing developments. If a fire station can be built at any point in the coordinate system, at which point would it be equidistant from all three developments? Choose the correct choice: A) (3,7) B) (5,3) C) (3,4) D) (6,4) E) (5,5)
All points equidistant from O and Q lie on the line x = 6, so the fire station should lie on this line.   All points equidistant from O and P lie on the line y = 4, so the fire station should lie on this line.   These two intersect at (6,4) and that will be the point equidistant from all 3 points.   The answer is (6,4).
<result>D</result>
In a rectangular coordinate system, points O (2,2), P (2,6), and Q (10,2) represent the sites of three proposed housing developments. If a fire station can be built at any point in the coordinate system, at which point would it be equidistant from all three developments?