# A triangle has corners at (1 ,2 ), (9 ,6 ), and (8 ,5 ). How far is the triangle's centroid from the origin?

Nov 10, 2016

The distance is $= 7.4$

#### Explanation:

The centroid of a triangle $\left({x}_{g} , {y}_{g}\right)$
is given by ${x}_{g} = \frac{{x}_{1} + {x}_{2} + {x}_{3}}{3}$
and ${y}_{g} = \frac{{y}_{1} + {y}_{2} + {y}_{3}}{3}$

Therefore ${x}_{g} = \frac{1 + 9 + 8}{3} = 6$
and ${y}_{g} = \frac{2 + 6 + 5}{3} = \frac{13}{3}$

The distance from the origin $= \sqrt{{x}_{g}^{2} + {y}_{g}^{2}} = \sqrt{36 + \frac{169}{9}}$
$= \frac{\sqrt{493}}{3} = \frac{22.2}{3} = 7.4$