Answer
See proof
Work Step by Step
First side:
Between $(-7/2,4)$ and $(-5/2,2)$:
$m=\frac{2-4}{-\frac{5}{2}-(-\frac{7}{2})}=-2$
The opposing side: $(1,3)$ and $(2,1)$:
$m=\frac{1-3}{2-1}=-2$
$\Rightarrow $ same slope.
Likewise, we can now show the sides $(-7/2,4)$ and $(1,3)$:
$m=\frac{3-4}{1-(-\frac{7}{2})}=-4.5$
as well as the side between $(-5/2,2)$ and $(2,1)$:
$m=\frac{1-2}{2-(-\frac{5}{2})}=-4.5$
$\Rightarrow$ same slope.
$\Rightarrow$ parallelogram.
