Answer
See below.
Work Step by Step
Step 1. Let $A(1,-1), B(4,1), C(2,2),D(5,4)$ are the given vertices, we have the slopes $m_{AB}=\frac{1+1}{4-1}=\frac{2}{3}$, $m_{CD}=\frac{4-2}{5-2}=\frac{2}{3}$, thus $AB\parallel CD$,
Step 2. Similarly, $m_{AC}=\frac{2+1}{2-1}=3$, $m_{BD}=\frac{4-1}{5-4}=3$, thus $AC\parallel BD$,
Step 3. We can conclude that the quadrilateral is a paralelogram.
