In the xy-plane, if points (5, 2), (2, 5), and (-2, -5) are the vertex

My approach to this is to start by making a sketch and plotting the three points and labelling them A, B, and C. We know that two of them must form one side of the parallelogram and the remaining one will form the parallel side along with whatever point is the remaining vertex.

Let's say AandB form a side. There are two options for where to place the unnamed vertex D such that CD is parallel to AB and D is the same distance from C that B is from A. So, that's two.

Let's say AandC form a side. There are two options for where to place the unnamed vertex D such that BD is parallel to AC and D is the same distance from B that C is from A. But one of them is the same one of the ones we already found. So, that's one more for a running total of three.

Let's say BandC form a side. There are two options for where to place the unnamed vertex D such that AD is parallel to BC and D is the same distance from A that C is from B. But both of them are the same as ones we've already found. So, our total is three.

Answer choice C.