Geometry

Question Analysis

This question focuses on applying the properties of the centroid of a triangle. The key is to use the fact that the centroid divides each median in a specific ratio to find the length of  given the length of .

 

Key Concept Explanation

The centroid of a triangle is the point of intersection of the medians. A median is a line segment that connects a vertex of the triangle to the mid - point of the opposite side. The centroid divides each median in the ratio , where the segment from the vertex to the centroid is twice as long as the segment from the centroid to the mid - point of the side.

 

Step - by - Step Solution

1. Recall the centroid - median property: Since  is the centroid of , the median  is divided by  such that , which means  and . So,

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