# A triangle has corners at (9 ,5 ), (2 ,7 ), and (3 ,2 ). How far is the triangle's centroid from the origin?

The distance of centroid from the origin is $6.6$ unit.
The co-ordinate $\left(x , y\right)$ of centroid is x=(x_1+x_2+x_3)/3 and y=(y_1+y_2+y_3)/3 or x= (9+2+3)/3=14/3 ; y=(5+7+2)/3 =14/3
The distance of centroid $\left(\frac{14}{3} , \frac{14}{3}\right)$ from the origin $\left(0 , 0\right)$ is $d = \sqrt{{\left(\frac{14}{3} - 0\right)}^{2} + {\left(\frac{14}{3} - 0\right)}^{2}} = \sqrt{\frac{196}{9} + \frac{196}{9}} = 6.6 u n i t$[Ans]