# A triangle has corners at (7 ,2 ), (6 ,7 ), and (3 ,1 ). How far is the triangle's centroid from the origin?

Jul 23, 2017

The distance is $= 6.3$

#### Explanation:

The centroid is

$\left({x}_{c} , {y}_{c}\right) = \left(\frac{{x}_{1} + {x}_{1} + {x}_{3}}{3} , \frac{{y}_{1} + {y}_{2} + {y}_{3}}{3}\right)$

Therefore,

$\left({x}_{c} , {y}_{c}\right) = \left(\frac{7 + 6 + 3}{3} , \frac{2 + 7 + 1}{3}\right) = \left(\frac{16}{3} , \frac{10}{3}\right)$

The distance from the origin is

${d}_{C} = \sqrt{{\left({x}_{c}\right)}^{2} + {\left({y}_{c}\right)}^{2}}$

$= \sqrt{{\left(\frac{16}{3}\right)}^{2} + {\left(\frac{10}{3}\right)}^{2}}$

$= \frac{\sqrt{356}}{3}$

$= 6.3$