# A triangle has corners at (2 ,4 ), (8 ,6 ), and (7 ,9 ). How far is the triangle's centroid from the origin?

##### 1 Answer
Nov 1, 2016

The distance is $\frac{\sqrt{650}}{3}$

#### Explanation:

Let point O = the centroid = $\left({O}_{x} , {O}_{y}\right)$

${O}_{x} = \frac{2 + 8 + 7}{3} = \frac{17}{3}$

${O}_{y} = \frac{4 + 6 + 9}{3} = \frac{19}{3}$

The distance, d, from the origin is:

$d = \sqrt{{\left(\frac{17}{3} - 0\right)}^{2} + {\left(\frac{19}{3} - 0\right)}^{2}} = \frac{\sqrt{650}}{3}$