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slamgirl [31]
4 years ago
14

In triangle ABC, point D is the centroid, and BD = 6. Find BE.

Mathematics
1 answer:
pshichka [43]4 years ago
6 0

Given:

In triangle ABC, point D is the centroid, and BD = 6.

To find:

The measure of side BE.

Solution:

We know that the centroid divides each median in 2:1.

In the given figure BE is a median and point D is the centroid. It means point D divides the segment BE in 2:1.

Let BD and DE are 2x and x respectively.

We have, BD = 6 units.

2x=6

x=\dfrac{6}{2}

x=3

Now,

BE=BD+DE

BE=6+x

BE=6+3

BE=9

Therefore, the measure of side BE is 9 units.

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A)

\begin{aligned}&A B=\sqrt{(2-0)^{2}+(5-2)^{2}}=\sqrt{13} \\&B C=\sqrt{(-1-2)^{2}+(7-5)^{2}}=\sqrt{13} \\&C A=\sqrt{(-1-0)^{2}+(7-2)^{2}}=\sqrt{26} \\&A B=\sqrt{13}, B C=A B=\sqrt{13}, C A=\sqrt{26}\end{aligned}

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Slope of CA line = m₃=-5

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