Answer
See explanations.
Work Step by Step
We need to show that the opposite sides are parallel and adjacent sides are perpendicular.
Step 1. Let A, B, C, D be the vertices $A(-1,0),B(2,3),C(1,-2),D(4,1)$
Step 2. Find slopes of each side: $m_{AB}=\frac{0-3}{-1-2}=1$, $m_{CD}=\frac{-2-1}{1-4}=1$, $m_{AC}=\frac{0+2}{-1-1}=-1$, $m_{BD}=\frac{3-1}{2-4}=-1$,
Step 3. Since $AB\parallel CD$ and $AC\parallel BD$, we have a parallelogram.
Step 4. Since $AB\perp AC$ and $CD\perp BD$, we have a rectangle.
