Question: A median of a triangle is a segment joining a vertex to the midpoint of the opposite side. Show that the centroid of a triangle

A median of a triangle is a segment joining a vertex to the midpoint of the opposite side. Show that the centroid of a triangle lies on each of its medians, at a distance two-thirds down from the vertex. Then use this fact to prove that the three medians intersect at a single point. Simplify the calculation by assuming that one vertex lies at the origin and another on the x-axis.

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Orient the triangle by placing one vertex at 0 0 and the long side of the triangle along the xaxis L... View full answer

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