G is the centroid, AG = 9, find GD

Step by step

The question

Question: A D is a median of triangle A B C and G is where the medians meet, with AG = 9: find GD.

1 Use the median rule

A median goes from a corner to the middle of the opposite side.

D is the middle of B C.

The three medians all meet at one point, G.

It is called the centroid.

G cuts each median into 2 parts and 1 part: the long part from the corner.

2 Find one part

A G is 2 parts.

One part is 9 divided by 2: 4.5.

Careful!

G is not the middle of the median.

A G is 2 parts out of 3.

3 Find GD

GD is 1 part: 4.5.

4 Check

Let's check: A G plus G D is 13.5, the whole median.

And A G is twice G D.

So it is right!

Let's look back.

First: use the median rule.

Then: find one part.

Then: find GD.

Last: check.