16.10 Given that the base $AB$ of $\triangle ABC$ is of fixed length and position, when the vertex $C$ moves along a straight line, then the intersection of its three medians moves on what kind of figure?
(A) A circle.
(B) A parabola.
(C) An ellipse.
(D) A straight line.
(E) None of the above curves.
(13th American High School Mathematics Examination, 1962)
[Solution] Let the vertex $C$ of $\triangle ABC$ move to $C_{1}$ on line $l_{1}$. If $G$ is the centroid of $\triangle ABC$ and $G_{1}$ is the centroid of $\triangle ABC_{1}$,  
by the centroid theorem of a triangle, we have
$$
C G=\frac{2}{3} C M, \quad C_{1} G_{1}=\frac{2}{3} C_{1} M,
$$

thus $G G_{1} \parallel C C_{1}$.
That is, when $C$ moves on $l_{1}$, the centroid $G$ of the triangle moves on a line $l_{2}$ parallel to $l_{1}$.
Therefore, the answer is $(D)$.