Answer
See below.
Work Step by Step
Step 1. Let $A(-1,0), B(2,3), C(1,-2),D(4,1)$ are the given vertices, we have the slopes $m_{AB}=\frac{3-0}{2+1}=1$, $m_{CD}=\frac{1+2}{4-1}=1$, thus $AB\parallel CD$,
Step 2. Similarly, $m_{AC}=\frac{0+2}{-1-1}=-1$, $m_{BD}=\frac{3-1}{2-4}=-1$, thus $AC\parallel BD$,
Step 3. We can conclude that the quadrilateral is a paralelogram.
Step 4. Furthermore, $m_{AB}\cdot m_{AC}=m_{CD}\cdot m_{BD}=-1$, thus $AB\perp AC, CD\perp BD$, thus we have a rectangle.
