Answer: Yes, the quadrilateral ABCD is a TRAPEZOID.
Step-by-step explanation: Given that the co-ordiantes of the vertices of quadrilateral ABCD are A(–4, –5), B(–3, 0), C(0, 2), and D(5, 1).
We are to determine whether the quadrilateral ABCD is a trapezoid or not.
<u><em>TRAPEZOID:</em></u><em> It is a quadrilateral having one pair of opposite sides parallel.</em>
We will find the slopes of all the sides AB, BC, CD and DA of quadrilateral ABCD as follows:

Since the slopes of sides BC and DA are equal, so the sides are parallel.
Hence, the quadrilateral ABCD has one pair of opposite sides parallel.
Thus, quadrilateral ABCD is a TRAPEZOID.