A Quadrilateral

Question

I've tried this question repeatedly? Can any person who knows the analytic geometry field answer this?

Quadrilateral PQRS has vertices P(3, 2), Q(0, 4), R(-2, 1) and S(1, -1) 
a) Verify that quadrilateral PQRS is a square.
b) Find the perimeter of the rectangle.

Answer 1

You need to find the side lengths, using the distance formula.

The perimeter of the figure is the sum of PQ + QR + RS + SP.

If all four of these quantities have the same value, it could be a square.

 

Further (complete proof) of the squareness would be that the two diagonals are equal: Is QS = PR?

 

Other attributes follow (but the above is sufficient), namely the four angles of the quadrilateral are all rt. angles, the diagonals are mutually perpendicular and they bisect each other.