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

##### 1 Answer
May 5, 2016

Distance of centroid from origin is (approximately) $6.15$ units

#### Explanation:

The centroid of a triangle with corners at $\left({x}_{1} , {y}_{1}\right) , \left({x}_{2} , {y}_{2}\right) , \mathmr{and} \left({x}_{3} , {y}_{3}\right)$ can be located using the formula
$\textcolor{w h i t e}{\text{XXX}} \left({x}_{c} , {y}_{c}\right) = \left(\frac{{x}_{1} + {x}_{2} + {x}_{3}}{3} , \frac{{y}_{1} + {y}_{2} + {y}_{3}}{3}\right)$

In this case
$\textcolor{w h i t e}{\text{XXX}} \left(c {x}_{c} , {y}_{c}\right) = \left(\frac{9 + 2 + 3}{3} , \frac{3 + 5 + 4}{3}\right) = \left(\frac{14}{3} , 4\right)$

The distance of the centroid at $\left(\frac{14}{3} , 4\right)$ and the origin at $\left(0 , 0\right)$
can be calculated using the Pythagorean Theorem as
$\textcolor{w h i t e}{\text{XXX}} d = \sqrt{{\left(\frac{14}{3}\right)}^{2} + {4}^{2}} \approx 6.15$