In triangle PQR, medians PX, QY, and RZ intersect at the centroid O. What is the ratio of the area of triangle PQO to the area of triangle PQR?

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Accepted Answer

1. The medians meet at centroid O, which divides each median in the ratio $2:1$ from the vertex.
2. The three medians cut the triangle into $6$ small triangles of equal area.
3. Triangle $PQO$ is made of $2$ of those equal small triangles.
4. So the area ratio is $2/6=1/3$, i.e. $1:3$.

FINAL_ANSWER: b

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