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

Nov 30, 2016

The distance $= 6.2$

#### Explanation:

If the corners of a triangle are $\left({x}_{1} , {y}_{1}\right) , \left({x}_{2} , {y}_{2}\right) \mathmr{and} \left({x}_{3} , {y}_{3}\right)$

Then, the coordinates of the centroid are

${x}_{c} = \frac{{x}_{1} + {x}_{2} + {x}_{3}}{3} = \frac{1 + 8 + 5}{3} = \frac{14}{3}$

${y}_{c} = \frac{{y}_{1} + {y}_{2} + {y}_{3}}{3} = \frac{1 + 2 + 9}{3} = \frac{12}{3} = 4$

The distance of the centroid from the origin is

$= \sqrt{{x}_{c}^{2} + {y}_{c}^{2}} = \sqrt{{14}^{2} / 9 + 16} = \frac{\sqrt{340}}{3} = 6.2$