Knowing 3 points of a figure, the fourth point can take how many values so that the given figure form a parallelogram. (GRE exam 9768 Q.42)

Question

I do not know how to solve it, could anyone give me a hint? or tell me if this question How to test whether a set of four points can form a parallelogram is useful in the solution or irrelevant?

Answer 1

As mentioned in the comment. The three given points form a $V$ of bottom $C$. The three cases are : 1) placing $D$ so $CA$ is diagonal $CB$ a side. 2) versa 1)

3) $CA$ and $CB$ are two sides.