# A triangle has corners at (6 ,1 ), (5 ,7 ), and (3 ,8 ). How far is the triangle's centroid from the origin?

##### 1 Answer
Jun 14, 2016

$\left(\frac{1}{3}\right) \sqrt{452} \cong 7.09 .$

#### Explanation:

Centroid $G$ is $G \left(\frac{6 + 5 + 3}{3} , \frac{1 + 7 + 8}{3}\right) = G \left(\frac{14}{3} , \frac{16}{3}\right)$, & the Origin $O$ is $O \left(0 , 0\right) .$

The distance $d$ between these points, using the distance formula,
$d = \sqrt{{\left(\frac{14}{3}\right)}^{2} + {\left(\frac{16}{3}\right)}^{2}} = \left(\frac{1}{3}\right) \sqrt{196 + 256} = \left(\frac{1}{3}\right) \sqrt{452} \cong \left(\frac{1}{3}\right) \left(21.26\right) \cong 7.09 .$