In a rectangular coordinate system, points O (2,0), P (2,6), and Q (8,0) represent the sites of ...

In a rectangular coordinate system, points O (2,0), P (2,6), and Q (8,0) 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?

Quiz

Answer/Solution

(5,3)

Steps/Work

All points equidistant from O and Q lie on the line x = 5, so the fire station should lie on this line.
All points equidistant from O and P lie on the line y = 3, so the fire station should lie on this line.
These two intersect at (5,3) and that will be the point equidistant from all 3 points.
The answer is B.