Question

prove that the points A (2,3), B(-2,2),C(-1,-2) and D(3,-1) are the vertices of a square ABCD.

Answer 1

for that you can use the distance formula
first find the length of a b then BC then CD and then AD if all the sides are equal then it is not a square but it can become a parallelogram now
to prove that it is a square not a parallelogram you need to find the length of the diagonals that is AC and BD if they both are equal then you can say that the figure given is a square

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Answer 2

☝☝☝ is a correct answer of your question