# A triangle has corners at (7 ,9 ), (4 ,1 ), and (3 ,8 ). How far is the triangle's centroid from the origin?

Aug 29, 2017

The centroid is $7.6$ unit far from origin.

#### Explanation:

Centroid $\left(x\right) = \frac{{x}_{1} + {x}_{2} + {x}_{3}}{3} = \frac{7 + 4 + 3}{3} = \frac{14}{3}$

Centroid $\left(y\right) = \frac{{y}_{1} + {y}_{2} + {y}_{3}}{3} = \frac{9 + 1 + 8}{3} = \frac{18}{3} = 6$

So centroid is at $\left(\frac{14}{3} , 6\right)$ and origin is $\left(0.0\right)$

Distance of centoid from origin is $d = \sqrt{{\left({x}_{1} - {x}_{2}\right)}^{2} + {\left({y}_{1} - {y}_{2}\right)}^{2}}$

or $d = \sqrt{{\left(\frac{14}{3}\right)}^{2} + {6}^{2}} \approx 7.6$ unit

The centroid is $7.6$ unit far from origin. [Ans]