# A triangle has corners at (6 ,7 ), (2 ,6 ), and (1 ,5 ). How far is the triangle's centroid from the origin?

Oct 15, 2017

Distance between centroid and origin is
d = sqrt5 = 2.2361

#### Explanation:

Coordinates of centroid:
$x = \frac{x 1 + x 2 + x 3}{3} , y = \frac{y 1 + y 2 + y 3}{3}$

$x = \frac{6 + 2 + 1}{3} = 3$
$y = \frac{7 + 6 + 5}{3} = 2$
Coordinates of centroid of the triangle (1,2)#

Coordinates of origin (0,0).
Distance between centroid and origin is
$d = \sqrt{{\left(1 - 0\right)}^{2} + {\left(2 - 0\right)}^{2}} = \sqrt{5} = 2.2361$