Answer
a.
See image, below.
b.
The midpoint of $AC$ is $(\displaystyle \frac{5}{2},3)$
The midpoint of $BD$ is also $(\displaystyle \frac{5}{2},3)$.\\\\
c.
Since they have a common midpoint, the diagonals bisect each other.
Work Step by Step
b.
The midpoint of $AC$ is $(\displaystyle \frac{-2+7}{2}, \displaystyle \frac{-1+7}{2})=(\frac{5}{2},3)$,
The midpoint of $BD$ is $(\displaystyle \frac{4+1}{2}, \displaystyle \frac{2+4}{2})=(\frac{5}{2},3)$.
c.
Since they have the same midpoint, we conclude that the diagonals bisect each other.
