# A triangle has corners at (6 ,7 ), (2 ,6 ), and (5 ,2 ). How far is the triangle's centroid from the origin?

Feb 4, 2018

Distance of centroid from origin is

$O G = d = \sqrt{{\left(\frac{13}{3}\right)}^{2} + {5}^{2}} = \textcolor{p u r p \le}{6.6165}$

#### Explanation:

Formula for finding the centroid coordinates.

${G}_{x} = \frac{x 1 + x 2 + x 3}{3} = \frac{6 + 2 + 5}{3} = \frac{13}{3}$

${G}_{y} = \frac{y 1 + y 2 + y 3}{3} = \frac{7 + 6 + 2}{3} = 5$

Centroid coordinates $G \left(\frac{13}{3} , 5\right)$

Distance from origin $O \left(0 , 0\right)$ is

$d = \sqrt{{\left(\frac{13}{3}\right)}^{2} + {5}^{2}} = \textcolor{p u r p \le}{6.6165}$