# A triangle has corners at (4 ,1 ), (8 ,3 ), and (3 ,5 ). How far is the triangle's centroid from the origin?

Jan 10, 2018

Triangle’s centroid is 5.83 away from origin.

#### Explanation:

Centroid
$G \left(x\right) = \frac{x 1 + x 2 + x 3}{3} = \frac{4 + 8 + 3}{3} = 5$

$G \left(y\right) = \frac{y 1 + y 2 + y 3}{3} = \frac{1 + 3 + 5}{3} = 3$

Coordinates of centroid G is $\left(5 , 3\right)$

Distance from origin $d = \sqrt{{x}^{2} + y 2} = \sqrt{{5}^{2} + {3}^{2}} \approx \textcolor{red}{5.83}$