# A triangle has corners at (5 ,1 ), (7 ,2 ), and (6 ,3 ). How far is the triangle's centroid from the origin?

Dec 18, 2017

Centroid is 6.3246 from the origin

#### Explanation:

Coordinates of Centroid of a triangle is obtained as below :
Let G be the centroid and the coordinates G(x), G(y).

X coordinate of centroid Gx) = (x_1 + x_2 + x_3) / 3 &
Y coordinate of centroid $G \left(y\right) = \frac{{y}_{1} + {y}_{2} + {y}_{3}}{3}$

$G \left(x\right) = \frac{5 + 7 + 6}{3} = 6$

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

Distance ‘ D’ of centroid ‘G’ from origin is given by
$D = \sqrt{{\left(G \left(x\right) - 0\right)}^{2} + {\left(G \left(y\right) - 0\right)}^{2}}$

$D = \sqrt{G {\left(x\right)}^{2} + G {\left(y\right)}^{2}} = \sqrt{{6}^{2} + {2}^{2}} = \sqrt{40} = 6.3246$