# A triangle has corners at (4 ,3 ), (8 ,6 ), and (7 ,1 ). How far is the triangle's centroid from the origin?

Oct 1, 2016

$d = \frac{\sqrt{461}}{3}$

#### Explanation:

The centroid (h, k) is

$h = \frac{4 + 8 + 7}{3} = \frac{19}{3}$

$k = \frac{3 + 6 + 1}{3} = \frac{10}{3}$

The distance, d, is:

$d = \sqrt{{\left(\frac{19}{3}\right)}^{2} + {\left(\frac{10}{3}\right)}^{2}}$

$d = \frac{\sqrt{461}}{3}$