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

Feb 16, 2018

Distance of centroid from origin is $\vec{G O} \approx \textcolor{g r e e n}{7.341}$ units

#### Explanation:

Given the coordinates of the three vertices of the triangle.

$A \left(7 , 3\right) , B \left(4 , 4\right) , C \left(6 , 7\right)$

To find centroid G and it’s distance from origin.

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

$G \left(x\right) = \frac{7 + 4 + 6}{3} = \frac{17}{3}$

$G \left(y\right) = \frac{3 + 4 + 7}{3} = \frac{14}{3}$

Distance centroid from origin can be arrived at by using distance formula

$d = \sqrt{{\left(x 2 - x 1\right)}^{2} + {\left(y 2 - y 1\right)}^{2}}$

$\vec{G O} = \sqrt{{\left(\frac{17}{3}\right)}^{2} + {\left(\frac{14}{3}\right)}^{2}}$ coordinates of origin is (0,0)

$\vec{G O} \approx \textcolor{g r e e n}{7.341}$ units