# A triangle has corners at (4 ,1 ), (8 ,3 ), and (5 ,8 ). How far is the triangle's centroid from the origin?

Jan 27, 2017

The distance is $= 6.9$

#### Explanation:

If we have a triangle has corners $\left({x}_{1} , {y}_{1}\right)$ ; $\left({x}_{2} , {y}_{2}\right)$ and $\left({x}_{3} , {y}_{3}\right)$

The coordinates of the centroid are

${x}_{c} = \frac{{x}_{1} + {x}_{2} + {x}_{3}}{3}$

and

${y}_{c} = \frac{{y}_{1} + {y}_{2} + {y}_{3}}{3}$

and the distance from the orogin is

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

Here, we have

${x}_{c} = \frac{4 + 8 + 5}{3} = \frac{17}{3}$

${y}_{c} = \frac{1 + 3 + 8}{3} = 4$

Therefore,

$O C = \sqrt{{\left(\frac{17}{3}\right)}^{2} + \left({4}^{2}\right)} = \sqrt{48.11} = 6.9$