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Formulate and describe a general instruction for the construction of a square when you are given two adjacent corners.

Formulate and describe a general instruction for the construction of a square when you are given two opposite corners.

Decide whether any of the collections of points below form a square.
If so, which ones?
Can you do this without plotting the points on a grid?

1. $(8,3)$, $(7,8)$, $(2,7)$, $(3,2)$
2. $(3,3)$, $(7,4)$, $(8,8)$, $(4,7)$
3. $(16,19)$, $(18,22)$, $(21,20)$, $(19,17)$
4. $(4,20)$, $(21,19)$, $(20,2)$, $(3,3)$

Explain how you decided.