Question

in ABC, G is the centroid and BE = 9 Find BG and GE.

Answer 1

The centroid is the intersection of the 3 medians of a triangle.

Also,

The centroid divides each median in the ratio 2: 1.

Now, looking at the figure, BE is divided in the ratio BG to GE is 1:2 format.

Given BE = 9

If we divide it by 1+2 = 3 parts, each part is:

9 / 3 = 3

Thus,

BG = 1 part = 1 x 3 = 3

GE = 2 part = 2 x 3 = 6

Answer:

BG = 3

GE = 6

Note:

$\begin{gathered} \frac{BG}{BE}=\frac{1}{3} \\ BG\cdot3=BE \\ BG\cdot3=9 \\ BG=\frac{9}{3} \\ BG=3 \end{gathered}$

Note:

$\begin{gathered} \frac{GE}{BE}=\frac{2}{3} \\ 3\cdot GE=2\cdot BE \\ 3\cdot GE=2(9) \\ 3\cdot GE=18 \\ GE=\frac{18}{3} \\ GE=6 \end{gathered}$