# A triangle has corners at (5 ,2 ), (4 ,6 ), and (3 ,8 ). How far is the triangle's centroid from the origin?

Nov 19, 2016

The distance, $d = \sqrt{{\left(4 - 0\right)}^{2} + {\left(\frac{16}{3} - 0\right)}^{2}} = \frac{20}{3}$

#### Explanation:

Please see this reference Coordinates of the centroid of a triangle

From the reference webpage, we see that the centroid, point $O = \left({O}_{x} , {O}_{y}\right)$:

${O}_{x} = \frac{5 + 4 + 3}{3} = 4$

${O}_{y} = \frac{2 + 6 + 8}{3} = \frac{16}{3}$

The distance from the center is:

$d = \sqrt{{\left(4 - 0\right)}^{2} + {\left(\frac{16}{3} - 0\right)}^{2}} = \frac{20}{3}$