Just Opposite

A and C are the opposite vertices of a square ABCD, and have coordinates (a,b) and (c,d), respectively. What are the coordinates of the vertices B and D? What is the area of the square?

Beelines

Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?

A Tilted Square

The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?