# A triangle has corners at (1 ,9 ), (5 ,4 ), and (6 ,8 ). How far is the triangle's centroid from the origin?

May 8, 2017

The distance is $= 8.06$

#### Explanation:

Let $A B C$ be the triangle

$A = \left(1 , 9\right)$

$B = \left(5 , 4\right)$

$C = \left(6 , 8\right)$

The centroid of triangle $A B C$ is

${C}_{c} = \left(\frac{1 + 5 + 6}{3} , \frac{9 + 4 + 8}{3}\right) = \left(\frac{12}{3} , \frac{21}{3}\right) = \left(4 , 7\right)$

The distance of the centroid from the origin is

$= \sqrt{{4}^{2} + {7}^{2}}$

$= \sqrt{16 + 49}$

$= \sqrt{65}$

$= 8.06$