1962 AHSME Problem 15

Given \triangle ABC with base AB fixed in length and position. As the vertex C moves on a straight line, the intersection point of the three medians moves on:

\textbf{(A)}\ \text{a circle} \qquad \textbf{(B)}\ \text{a parabola} \qquad \textbf{(C)}\ \text{an ellipse} \qquad \textbf{(D)}\ \text{a straight line}\qquad \textbf{(E)}\ \text{a curve here not listed}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.