# A triangle has corners at (3 ,4 ), (6 ,7 ), and (2 ,8 ). How far is the triangle's centroid from the origin?

Apr 24, 2017

$\frac{1}{3} \sqrt{482} \approx 7.32 \text{ to 2 dec. places}$

#### Explanation:

$\text{the first step is to find the coordinates of the centroid}$

$\text{the coordinates are the " color(blue)"average}$ of the x and y coordinates of the given points.

${x}_{\text{centroid}} = \frac{1}{3} \left(3 + 6 + 2\right) = \frac{11}{3}$

${y}_{\text{centroid}} = \frac{1}{3} \left(4 + 7 + 8\right) = \frac{19}{3}$

$\text{coordinates of centroid } = \left(\frac{11}{3} , \frac{19}{3}\right)$

the distance between the centroid and the origin is.

d=sqrt((x_("centroid"))^2+(y_("centroid"))^2

$\textcolor{w h i t e}{d} = \sqrt{{\left(\frac{11}{3}\right)}^{2} + {\left(\frac{19}{3}\right)}^{2}}$

$\textcolor{w h i t e}{d} = \sqrt{\frac{121}{9} + \frac{361}{9}}$

$\textcolor{w h i t e}{d} = \sqrt{\frac{482}{9}}$

$\textcolor{w h i t e}{d} = \frac{1}{3} \sqrt{482} \approx 7.32 \text{ to 2 dec. places}$