Multiple choice

The centroid divides each median into two segments whose lengths are in the ratio ____.

  1. $1 : 2$
  2. $2 : 1$
  3. $2 : 3$
  4. $3 : 2$
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B Correct answer
Explanation

The centroid of a triangle divides each median in the ratio 2:1, measuring from the vertex to the midpoint of the opposite side.

AI explanation

A fundamental property of the centroid states that it is the point of concurrency of the medians and represents the center of mass of the triangle. Because it acts as the balancing point, the distance from the centroid to a vertex is always twice the distance from the centroid to the midpoint of the opposite side. Therefore, it divides each median into two segments with lengths in the ratio 2 to 1.

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