# A triangle has corners at (2 ,9 ), (4 ,2 ), and (5 ,1 ). How far is the triangle's centroid from the origin?

Oct 28, 2016

THe distance of the centroid from the origin is $5.43$

#### Explanation:

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

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

Let's call the centroid $\left({x}_{G} , {y}_{G}\right)$

Then the distance from the origin is $= \sqrt{{x}_{G}^{2} + {y}_{G}^{2}}$

The centroid is at $\left(\frac{2 + 4 + 5}{3} , \frac{9 + 2 + 1}{3}\right) = \left(\frac{11}{3} , 4\right)$

So the distance $= \sqrt{{11}^{2} / {3}^{2} + {4}^{2}} = 5.43$