Try to find a proof that only considers 2n 1 points recall

Question

We color each vertex of the plane red or blue. Let n ≥ 3 be an integer. Prove that there exist n points so that all these points and their centroid have the same color. Try to find a proof that only considers 2n + 1 points. (Recall that the centroid of a set of n points in a (vector) space, viewed as the vectors v₁, V₂, ..... , v_n is the point given by the vector (v_x + v₂ +..............+ v_n)/n.)