# A triangle has corners at (4 ,6 ), (3 ,9 ), and (2 ,5 ). How far is the triangle's centroid from the origin?

Oct 31, 2016

The distance of the centroid from the origin is $= 7.31$

#### Explanation:

Let the coordinates of the triangle be $\left({x}_{1} , {y}_{1}\right) , \left({x}_{2} , {y}_{2}\right) , \left({x}_{3} , {y}_{3}\right)$

Then the centroid is given by $\left(\frac{{x}_{1} + {x}_{2} + {x}_{3}}{3} , \frac{{y}_{1} + {y}_{2} + {y}_{3}}{3}\right)$

So the coordinates of the centroid are $\left(\frac{9}{3} , \frac{20}{3}\right)$
Let coordinates of centroid be $\left({x}_{c} , {y}_{c}\right)$

The distance from the origin is $\sqrt{{x}_{c}^{2} + {y}_{c}^{2}}$

So the distance is $= \sqrt{9 + \frac{400}{9}} = \sqrt{\frac{481}{9}} = 7.31$