Given four points A, B, C, and D.

Construct a square PQRS such that the points A, B, C, and D lie on lines
PQ, QR, RS, and SP respectively
or
describe the configuration of the four points where the construction is not possible.

Note: Don't confuse lines (of infinite extent) with sides (of finite extent).

I cannot find any configuration where the construction is not possible as long as the points are distinct.  I'm pretty sure it always will be. 

In the formulas I gave it is possible that the equation for m might have zero in the denominator.  But this just indicates the line is vertical.

Posted by Jer on 2013-01-10 11:27:52