# A triangle has corners at (4 ,1 ), (2 ,3 ), and (5 ,8 ). How far is the triangle's centroid from the origin?

Feb 10, 2018

Distance between centroid and origin is $\approx \textcolor{p u r p \le}{5.4263}$

#### Explanation:

Given : A(4,1), B(2,3), C(5,8)

Coordinates of centroid G

$G \left(x , y\right) = \frac{{x}_{a} + {x}_{a} + {x}_{c}}{3} , \frac{{y}_{a} + {y}_{b} + {y}_{c}}{3}$

${G}_{x} = \frac{4 + 2 + 5}{3} = \frac{11}{3}$

${G}_{y} = \frac{1 + 3 + 8}{3} = 4$

Distance between centroid G and origin O

$\vec{G O} = \sqrt{{\left(\frac{11}{3}\right)}^{2} + {4}^{2}} \approx \textcolor{p u r p \le}{5.4263}$