Chef and Railway Stations

Chef was working on building rail tracks connecting pairs of railway stations in a 2D Cartesian coordinate system. There are $N$ stations on the $x$-axis, with coordinates $x_1, x_2, \ldots, x_N$, and $M$ stations on the $y$-axis, with coordinates $y_1, y_2, \ldots, y_M$. Chef has completed his task and built a rail track (line segment) between each pair of stations. Now, Chef is wondering how