Answer: Both pairs of opposite sides are equal (PQ = RS = 5√2, QR = SP = 4√2), so PQRS is a parallelogram.
Distance formula: \(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\).
\[PQ=\sqrt{5^2+5^2}=\sqrt{50}=5\sqrt2\]
\[QR=\sqrt{4^2+(-4)^2}=\sqrt{32}=4\sqrt2\]
\[RS=\sqrt{(-5)^2+(-5)^2}=\sqrt{50}=5\sqrt2\]
\[SP=\sqrt{(-4)^2+4^2}=\sqrt{32}=4\sqrt2\]
PQ = RS and QR = SP. A quadrilateral whose opposite sides are equal is a parallelogram.