# A triangle has corners at (9 ,3 ), (4 ,4 ), and (3 ,7 ). How far is the triangle's centroid from the origin?

Oct 22, 2016

Distance of centroid from origin is $\frac{2 \sqrt{113}}{3}$

#### Explanation:

The centroid is located at $\overline{x} = \frac{\sum x}{3} , \overline{y} = \frac{\sum y}{3}$

And the distance from the origin is $\sqrt{{\overline{x}}^{2} + {\overline{y}}^{2}}$

So $\overline{x} = \frac{9 + 4 + 3}{3} = \frac{16}{3}$

And $\overline{y} = \frac{3 + 4 + 7}{3} = \frac{14}{3}$

The distance is $\sqrt{{\left(\frac{16}{3}\right)}^{2} + {\left(\frac{14}{3}\right)}^{2}} = \frac{\sqrt{256 + 196}}{3} = \frac{2 \sqrt{113}}{3}$