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G is the centroid of triangle ABC and D and E are the midpoints of line AB and line AC, respectively. line AG and line DE intersect at M. Find GM/GA.

 Feb 9, 2020
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The centroid of a triangle is found 2/3rds of the way from the vertex to the opposite side.

 

Since D and E are midpoints of two sides of a triangle, they create a line parallel to the base of the triangle (BC) and cut all transversals at their midpoints. Therefore, AM is 1/2 the way from the vertex to the opposite side.

 

This means that MG is (2/3 - 1/2)  =  1/6th the distance.

 

GM/GA  =  (1/6) / (2/3)  =  1/4

 Feb 10, 2020

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