# A triangle has corners at (1 ,9 ), (7 ,8 ), and (4 ,3 ). How far is the triangle's centroid from the origin?

Jan 30, 2018

Distance of centroid from origin $\textcolor{g r e e n}{O G = 7.7746}$

#### Explanation:

Coordinates of centroid is obtained using the formula

$G = \frac{{A}_{x} + {B}_{x} + {C}_{x}}{3} , \frac{{A}_{y} + {B}_{y} + {C}_{y}}{3}$

$G = \frac{1 + 7 + 4}{3} , \frac{9 + 8 + 3}{3}$

$G \left(4 , \frac{20}{3}\right)$

We have to find OG where O is the origin with coordinates (0,0)

Using distance formula,

$O G = \sqrt{{\left(4 - 0\right)}^{2} + {\left(\left(\frac{20}{3}\right) - 0\right)}^{2}} \approx 7.7746$