# A triangle has corners at (7 ,1 ), (8 ,2 ), and (5 ,9 ). How far is the triangle's centroid from the origin?

The distance of centroid from the origin is $7.77 \left(2 \mathrm{dp}\right)$ unit
The co-ordinate of centroid of the triangle is$x = \frac{{x}_{1} + {x}_{2} + {x}_{3}}{3} = \frac{7 + 8 + 5}{3} = \frac{20}{3} , y = \frac{{y}_{1} + {y}_{2} + {y}_{3}}{3} = \frac{1 + 2 + 9}{3} = 4$i.e $\left(\frac{20}{3} , 4\right)$; The distance of centroid$\left(\frac{20}{3} , 4\right)$ from the origin$\left(0 , 0\right)$ is $\sqrt{{\left(\frac{20}{3} - 0\right)}^{2} + {\left(4 - 0\right)}^{2}} = \sqrt{\frac{400}{9} + 16} = \sqrt{\frac{544}{9}} = 7.77 \left(2 \mathrm{dp}\right)$unit[Ans]