# A triangle has corners at (5 ,6 ), (2 ,7 ), and (3 ,4 ). How far is the triangle's centroid from the origin?

Nov 26, 2016

$d = 6.58 \text{ unit}$

#### Explanation:

$A = \left(5 , 6\right)$

$B = \left(2 , 7\right)$

$C = \left(3 , 4\right)$

$\text{Centroid :} D \left(x , y\right)$

$x = \frac{5 + 2 + 3}{3} = \frac{10}{3} = 3.33$

$y = \frac{6 + 7 + 4}{3} = \frac{17}{3} = 5.67$

$D \left(3.33 , 5.67\right)$

$O D = d$

$d = \sqrt{{\left(3.33 - 0\right)}^{2} + {\left(5.67 - 0\right)}^{2}}$

$d = \sqrt{{3.33}^{2} + {5.67}^{2}}$

$d = \sqrt{11.09 + 32.15}$

$d = \sqrt{43.24}$

$d = 6.58$