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).

(In reply to It's all relative (partial spoiler?) by Steve Herman)

Steve,

"... if any three points are collinear and distinct, then the construction is impossible."

Did you miss the note; lines not sides.

Posted by Bractals on 2013-01-08 18:47:14