Question

In ACE, G is the centroid and BE=9. Find BG and GE

Answer 1

BG = 1/3(BE) = 1/3 (9) = 3
GE = 2/3(BE) = 2/3 (9) = 6

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Answer 2

The centroid point G divides the segment $\overline{BE}$ in the ration 2 : 1, such that

$\overline{GE}$ is twice the length of $\overline{BE}$.

• $\underline{\mathrm{\overline{BG} \ is \ 3 \ and \ \overline{GE} \ is \ 6}}$

Reasons:

The given parameter are;

The centroid of ΔACE = Point G

The length of BE = 9

Required:

The length of $\overline{BG}$ and $\overline{GE}$

Solution:

By centroid relationship, we have;

$\overline{BG} = \mathbf{ \dfrac{1}{3} \times \overline{BE}}$

Therefore;

$\overline{BG} = \dfrac{1}{3} \times 9 = 3$

$\overline{BG}$ = 3

Similarly, by the relationship between the centroid, G, $\overline{GE}$ and $\overline{BE}$ we have;

$\overline{GE} =\mathbf{ \dfrac{2}{3} \times \overline{BE}}$

Which gives;

$\overline{GE} = \dfrac{2}{3} \times9 = 6$

$\overline{GE}$ = 6

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