# A triangle has corners at (5 ,2 ), (4 ,6 ), and (8 ,5 ). How far is the triangle's centroid from the origin?

Oct 5, 2016

The distance is $\approx 7.13$

#### Explanation:

Centroid coordinates given the vertices is a reference for the equations that I will use.

Let $\left({O}_{x} , {O}_{y}\right)$ be the centroid and $\left({A}_{x} , {A}_{y}\right)$, $\left({B}_{x} , {B}_{y}\right)$, and00 $\left({C}_{x} , {C}_{y}\right)$ be the vertices then:

${O}_{x} = \frac{{A}_{x} + {B}_{x} + {C}_{x}}{3}$

and

${O}_{y} = \frac{{A}_{y} + {B}_{y} + {C}_{y}}{3}$

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

and

${O}_{y} = \frac{2 + 6 + 5}{3} = \frac{13}{3}$

The distance from the origin is:

d = sqrt((17/3)² + (13/3)²)

$d \approx 7.13$