# A triangle has corners at (1 ,9 ), (3 ,7 ), and (6 ,2 ). How far is the triangle's centroid from the origin?

Dec 1, 2016

The distance is $\frac{\sqrt{424}}{3}$

#### Explanation:

Here is a reference that tell you how to compute the centroid of a triangle given the coordinates of its vertices

${O}_{x} = \frac{1 + 3 + 6}{3} = \frac{10}{3}$

${O}_{y} = \frac{9 + 7 + 2}{3} = 6$

The centroid is $\left(\frac{10}{3} , 6\right)$

The distance from the origin is:

$d = \sqrt{{\left(\frac{10}{3}\right)}^{2} + {6}^{2}} = \frac{\sqrt{424}}{3}$