A triangle has corners at (1 ,9 ), (3 ,8 ), and (4 ,5 ). How far is the triangle's centroid from the origin?

Jan 18, 2017

Centroid $\left(\frac{8}{3} , \frac{22}{3}\right)$
Distance from the centre $\frac{\sqrt{548}}{3}$

Explanation:

The coordinates of the centroid would be $\frac{1 + 3 + 4}{3} , \frac{9 + 8 + 5}{3}$, that is $\left(\frac{8}{3} , \frac{22}{3}\right)$

Distance from the center (0,0) would be $\sqrt{{\left(\frac{8}{3}\right)}^{2} + {\left(\frac{22}{3}\right)}^{2}}$

$\sqrt{\frac{548}{9}} = \frac{\sqrt{548}}{3}$