In triangle ACE, G is the centroid and BE=9. Set up equations to find BG and GE, Then find BG and GE?

1 Answer

• Where is B located? I will need to assume that B is located at the midpoint of side AC, in order to solve the problem.

  Under this assumption, BE is a median. Along any median, the centroid of a triangle is always located 2/3 of the way from the vertex to the midpoint of the opposite side, so the centroid G is 2/3 of the way from E to B.

  So we have GE = (2/3)BE.

  Furthermore, by segment addition, BG + GE = BE.

  Since BE = 9, GE = (2/3)(9) = 6.

  Then BG + 6 = 9, which gives BG = 3.

  Have a blessed, wonderful day!