G is the centroid of Delta ABC Find GF AF and AE SolutionThe

G is the centroid of Delta ABC. Find GF, AF, and AE.

Solution

The distance from a vertex to the centroid is twice the distance from the centroid to the midpoint of the opposite side.

BG = 2 GF

=> GF = 1/2 * BG

= 1/2 * 4

= 2

Since F is the midpoint of AC

AF = FC

=> AF = 9

AE = AG + GE

AG = 2 * GE

= 10

=> AE = 10 + 5

= 15