Given 4 coordinates from the perimiter of a square, can the square be constructed? I have a square, tilted at an unknown angle.
I am given 4 coordinates of the square. They lie on the perimeter, one per side. With these 4, and nothing else, am I able to determine the vertices of this square? 
An example of 4 coordinates: $(4,13)$, $(12,23)$, $(23,14)$, $(14,5)$.
Trial and improvement (guessing the gradient?) would be acceptable, but I'm not sure how to start, as the gradient can go up  to $X/0$, or undefined.

no. 
Suppose they  are the vertices of a square, they are the mid-points of the sides of another square rotated 45 degrees. 
