My professor gave us the hint that it was related to the area of the parallelogram formed by two vectors being their cross product, and also that we can say $y=(1-t)c + td$, which would be perfect if a, b, c, and d were vectors, but the statement $x \in [a,b], y \in [c,d]$ seems to indicate they are just scalars indicating positions on the x and y-axis.
Is there a different approach I'm not seeing?