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

Mar 23, 2018

$\approx 6.00$

#### Explanation:

The position of the centroid is

$\left(\frac{{x}_{1} + {x}_{2} + {x}_{3}}{3} , \frac{{y}_{1} + {y}_{2} + {y}_{3}}{3}\right) = \left(\frac{4 + 8 + 5}{3} , \frac{1 + 3 + 2}{3}\right) = \left(\frac{17}{3} , 2\right)$

The distance of this point from the origin is

$\sqrt{{\left(\frac{17}{3}\right)}^{2} + {2}^{2}} = \sqrt{\frac{289}{9} + 4} = \sqrt{\frac{325}{9}} \approx \sqrt{36.11} \approx 6.00$