10*. Equal masses are placed at the vertices of an arbitrary quadrilateral. Find the position of their centroid.
10. If $A B C D$ is the given quadrilateral, then the general formula for the position vector of the centroid is

$$
\vec{P}=\frac{\vec{A}+\vec{B}+\vec{C}+\vec{D}}{4}
$$

At the same time, denoting by $M_{1}, M_{2}, M_{3}, M_{4}$ the centroids of triangles $B C D, A C D, A B D$ and $A B C$, we obtain that $P$ is the point of intersection of the lines $M_{1} M_{3}$ and $M_{2} M_{4}^{+}$.