# A triangle has corners at (5 ,6 ), (4 ,7 ), and (8 ,9 ). How far is the triangle's centroid from the origin?

##### 1 Answer
Sep 3, 2016

The distance of the centroid from origin is $9.27 \left(2 \mathrm{dp}\right) u n i t$[

#### Explanation:

The co-ordinates of centroid is $\left(\frac{{x}_{1} + {x}_{2} _ x 3}{3} , \frac{{y}_{1} + {y}_{2} _ y 3}{3}\right) \mathmr{and} \left(\frac{5 + 4 + 8}{3} , \frac{6 + 7 + 9}{3}\right) \mathmr{and} \left(\frac{17}{3} , \frac{22}{3}\right)$. The distance of the centroid from origin$\left(0.0\right)$ is $d = \sqrt{{\left(\frac{17}{3} - 0\right)}^{2} + {\left(\frac{22}{3} - 0\right)}^{2}} = \sqrt{{\left(\frac{17}{3}\right)}^{2} + {\left(\frac{22}{3}\right)}^{2}} = 9.27 \left(2 \mathrm{dp}\right) u n i t$[Ans]