In the following, ct represents a constant:

Basic premise for equating the distance on gridlines: .

Applying to all points results in, , and . This ensures that the coordinate of the point of interest lies in the first quadrant and will lessen the use of absolute values while solving. Once solved, we can revert back to the original location by applying .

Assume the solution is below H and M but between them. This respectively for H and M implies that

The point with respect to S yields:

Using the H equation:

Therefore, .