I'd rather suggest you procede like this: (like for dot-product). The first factor is , and you can leave the second factor as such (or replace it by where is the middle of ). Do the same for , and sum both results to make appear.
The problem with your method is that you're using , which probably means for some point ? Thus you are introducing a new point, while you should be looking for relation between the four corner points only. In the situation of the problem, you should forbid yourself to write things like , which only make sense with respect to a given origin.