Show that there exists a line passing through one red point and one blue point such that the number of red points on one side of the line is equal to the number of blue points on the same side. Describe how to find such a line in $O(n\log n)$ time.
note: There are n red points and n blue points on the plane and no three points are collinear.
For this problem I don't know where to start. I know how to find the shortest distance between a pair of points in $n \log n$ time but for this problem is it like a similar algorithm? Any help is appreciated.