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?
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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 other two vertices?


What is the area of the square?


How generalisable are these results?