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.
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