Answer
Opposite sides of the four sided figure lie on parallel lines,
with one pair having slopes $-\displaystyle \frac{9}{5}$ and the other with $\displaystyle \frac{5}{9}.$
Work Step by Step
Use: $m=\displaystyle \frac{\text{change in y}}{\text{change in x}}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$, parallel lines have equal slopes.
Plot the points (see below).
The slope of the line passing through $(-3,6)$ and $(6,11)$ is
$m=\displaystyle \frac{11-6}{6-(-3)}=\frac{5}{9}$
The slope of the line passing through $(2,-3)$ and $(11,2)$ is
$m=\displaystyle \frac{2-(-3)}{11-2}=\frac{5}{9}$
So, we have one pair of parallel lines passing through opposite sides.
The slope of the line passing through $(-3,6)$ and $(2,-3)$ is
$m=\displaystyle \frac{-3-6}{2-(-3)}=\frac{-9}{5}$
The slope of the line passing through $(6,11)$ and $(11,2)$ is
$m=\displaystyle \frac{2-11}{11-6}=\frac{-9}{5}$,
... and we have another pair of parallel lines passing through opposite sides.
Opposite sides of the four sided figure lie on parallel lines,
with one pair having slopes $-\displaystyle \frac{9}{5}$ and the other with $\displaystyle \frac{5}{9}.$
