Answer: AB ∥ CD and BC ∥ DA (equal slopes), so ABCD is a parallelogram.
Slope \(=\dfrac{y_2-y_1}{x_2-x_1}\).
Slope of AB \(=\dfrac{2+7}{-1+4}=3\), slope of CD \(=\dfrac{-4-5}{5-8}=3\).
Slope of BC \(=\dfrac{5-2}{8+1}=\dfrac13\), slope of DA \(=\dfrac{-7+4}{-4-5}=\dfrac13\).
So line AB ∥ line CD and line BC ∥ line DA. Both pairs of opposite sides are parallel, hence □ABCD is a parallelogram.