If you draw m straight lines in the plane consisting of x_{1} parallel in one direction, x_{2} parallel in different direction ... and x_{n} parallel in another direction and no three of the lines meeting at a point, show that the number of intersection points is \sum_{i<j} x_{i}x_{j} = \frac{1}{2}\left[m^2 - \sum_{j = 1}^{k} x_{j}^2\right]