In a rectangular coordinate system, points O (2,2), P (2,12), 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 answer
A) (5,6)
B) (8,7)
C) (5,8)
D) (6,6)
E) (6,7)
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 = 7, so the fire station should lie on this line.   These two intersect at (6,7) and that will be the point equidistant from all 3 points.   The answer is (6,7).
<result>E</result>
In a rectangular coordinate system, points O (2,2), P (2,12), 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?