Balanced line for a 3-colored point set in the plane

In this note we prove the following theorem. For any three sets of points in the plane, each of n ≥ 2 points such that any three points (from the union of three sets) are not collinear and the convex hull of 3n points is monochromatic, there exists an integer k ε {1, 2, ..., n-1} and an open half-plane containing exactly k points from each set.