In triangle upper A upper C upper E, G is the centroid and BE = 9. Find BG and GE.
Triangle A C E is shown. Point B is on segment A C and a median connects points B and E. Point D is on segment C E and a median connects points D and A. Point F is on segment A E and a median connects points F and C. The medians intersect at the triangle's centroid, which is labeled as point G.
According to the centroid properties, the medians of a triangle divide each other in a ratio of 2:1.
Let's label the length of BG as x. Then, GE would be 2x because it is twice the length of BG.
Therefore, we have the equation:
x + 2x + 9 = AC
Combining like terms, we get:
3x + 9 = AC
Since we don't have any other information about the triangle, we can't determine the exact length of AC. However, we can say that the length of BG is one-third of AC.
Therefore, we can conclude that the length of BG is 1/3 of AC, and the length of GE is 2/3 of AC.