# A triangle has corners at (4 ,3 ), (2 ,6 ), and (7 ,1 ). How far is the triangle's centroid from the origin?

Feb 24, 2017

$\frac{\sqrt{269}}{3} \approx 5.47$

#### Explanation:

The coordinates of the centroid are the average of the $x \mathmr{and} y$ coordinates of the three vertices.

$\implies {x}_{c} = \frac{1}{3} \left(4 + 2 + 7\right) = \frac{13}{3}$

$\implies {y}_{c} = \frac{1}{3} \left(3 + 6 + 1\right) = \frac{10}{3}$

Coordinates of the centroid $= \left(\frac{13}{3} , \frac{10}{3}\right)$

Distance $D$ between the centroid and the origin :
$D = \sqrt{{\left(\frac{13}{3}\right)}^{2} + {\left(\frac{10}{3}\right)}^{2}} = \frac{\sqrt{269}}{3} \approx 5.47$