You would take the midpoint of opposite vertexes. Take the coordinates of A and C, the midpoint of that, then the midpoint of D to B. That is if the plane is say a square with ABCD, listed in order all around. This is if only it is a square. If a parallelogram, I think you take the midpoint A to D, and B to C. I dont really know if my answer is correct, I have geometry teacher that seems sketchy lol.
I have just created an excel sheet with 2 lines, using the 2-dimensional formula (from wiki):
As you can see, the result matches the intersection point.
The formula I gave is the most generic, which is for m dimensions and for 2 or more lines.
Based on your opening post, I thought you were asking for that.
After your current comment it appears that you don't need it.