The vertices of square wxyz have coordinates w(0,4), x(4,0), y(0,-4) and z(-4,0)

Are you asking which of these four are the answer to prove?

1.) PR≠QS, so PQRS is not a rectangle or a square. The slope of PR¯¯¯¯¯=1, and the slope of QS¯¯¯¯¯ =0, so PQRS is not a rhombus.

2.) PR=QS, so PQRS is a rectangle or a square. The slope of PR¯¯¯¯¯=1, and the slope of QS¯¯¯¯¯ =2, so PQRS is not a rhombus. PQ=QR=RS=SP=42–√, so PQRS is square.  

3.) PR=QS, so PQRS is a rectangle or a square. The slope of PR¯¯¯¯¯=0, and the slope of QS¯¯¯¯¯ is undefined, so PR¯¯¯¯¯⊥QS¯¯¯¯¯. PQRS is a square.

4.) PR≠QS, so PQRS is not a rectangle or a square. The slope of PR¯¯¯¯¯=1, and the slope of QS¯¯¯¯¯ =2, so PQRS is not a rhombus.

answer: -8.2562234e+13