Question

in CDE, J is the centroid. If JF=15 find EJ

Answer 1

From the figure, J is the centroid. Hence, the lines DH, FE and CG are medians.

Therefore, we can apply the 2/3 rule, that is, the centroid is 2/3 of the way from the vertex to the opposite midpoint.

In other words, we can write

$JE=\frac{2}{3}FE$

since, we know that FE=FJ+JE, we have

$JE=\frac{2}{3}(FJ+JE)$

and, from this equation we can find JE since FJ=15:

$JE=\frac{2}{3}(15+JE)$

The, we obtain

$\begin{gathered} JE=\frac{2}{3}(15)+\frac{2}{3}JE \\ JE-\frac{2}{3}JE=\frac{2}{3}(3\cdot5) \\ \end{gathered}$

in which we moved (2/3)JE to the left hand side and we wrote 15 as 3*5. Now, it reads

$\begin{gathered} \frac{3}{3}JE-\frac{2}{3}JE=2\cdot5 \\ \frac{1}{3}JE=10 \\ JE=3\cdot10 \\ JE=30 \end{gathered}$

Therefore, JE=EJ=30.