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

Mar 1, 2017

The distance is $= 8.01$

#### Explanation:

The 3 corners of the triangle is $\left(7 , 6\right)$, $\left(4 , 4\right)$, and $\left(6 , 7\right)$

The centroid is

${x}_{c} = \frac{7 + 4 + 6}{3} = \frac{17}{3}$

${y}_{c} = \frac{6 + 4 + 7}{3} = \frac{17}{3}$

The distance of the centroid from the origin is

$d = \sqrt{{\left(\frac{17}{3}\right)}^{2} + {\left(\frac{17}{3}\right)}^{2}}$

$= \frac{17}{3} \sqrt{2}$

$= 8.01$