# A triangle has corners at (3 ,4 ), (6 ,3 ), and (2 ,8 ). How far is the triangle's centroid from the origin?

Jul 15, 2017

See below.

#### Explanation:

The centroid of a triangle is the average of the vertices of that triangle, or:

$\left(\frac{{x}_{1} + {x}_{2} + {x}_{3}}{3} , \frac{{y}_{1} + {y}_{2} + {y}_{3}}{3}\right)$

So,

$\left(\frac{{x}_{1} + {x}_{2} + {x}_{3}}{3} , \frac{{y}_{1} + {y}_{2} + {y}_{3}}{3}\right) = \left(\frac{3 + 6 + 2}{3} , \frac{4 + 3 + 8}{3}\right) = \left(\frac{11}{3} , \frac{15}{3}\right) = \left(\frac{11}{3} , 5\right)$

The distance from the origin is just $\setminus \sqrt{{\left(\frac{11}{3}\right)}^{2} + {5}^{2}} = \setminus \frac{\sqrt{346}}{3}$