# A triangle has corners at (6 ,2 ), (4 ,3 ), and (5 ,1 ). How far is the triangle's centroid from the origin?

Sep 4, 2016

$\setminus \sqrt{29}$ units, anout $5.385$.

#### Explanation:

The centroud of a triangle is obtained from averaging the coordinates of the vertices:

Vertices -- $\left(\textcolor{b l u e}{6} , \textcolor{g o l d}{2}\right) , \left(\textcolor{b l u e}{4} , \textcolor{g o l d}{3}\right) , \left(\textcolor{b l u e}{5} , \textcolor{g o l d}{1}\right)$

Centroid -- $\left(\textcolor{b l u e}{\frac{6 + 4 + 5}{3}} , \textcolor{g o l d}{\frac{2 + 3 + 1}{3}}\right) = \left(\textcolor{b l u e}{5} , \textcolor{g o l d}{2}\right)$.

Then the distance from the origin to point $\left(a , b\right)$ is $\setminus \sqrt{{a}^{2} + {b}^{2}}$, thus:

$\setminus \sqrt{{5}^{2} + {2}^{2}} = \setminus \sqrt{29}$.