Let

be positive integers. Consider in a plane

two disjoint sets of points

and

consisting of

and

points, respectively, and such that no three points of the union

are collinear. Prove that there exists a straightline

with the following property: Each of the two half-planes determined by

on

(

not being included in either) contains exactly half of the points of

and exactly half of the points of
%V0
Let $n_1, n_2$ be positive integers. Consider in a plane $E$ two disjoint sets of points $M_1$ and $M_2$ consisting of $2n_1$ and $2n_2$ points, respectively, and such that no three points of the union $M_1 \cup M_2$ are collinear. Prove that there exists a straightline $g$ with the following property: Each of the two half-planes determined by $g$ on $E$ ($g$ not being included in either) contains exactly half of the points of $M_1$ and exactly half of the points of $M_2.$