# A triangle has corners at (6 ,3 ), (7 ,4 ), and (1 ,2 ). How far is the triangle's centroid from the origin?

##### 1 Answer
Jan 14, 2018

Distance of centroid from origin is

$O G = \sqrt{{\left(\frac{14}{3}\right)}^{2} + {3}^{2}} = \textcolor{b l u e}{5.5478}$

#### Explanation:

Centroid (g) is the concurrent point of the three medians of a triangle.

$g$ is one third distance from the mid point of the base and two thirds from the corresponding vertex.

Hence centroid (g) coordinates are calculated using the formula

${G}_{x} = \frac{{x}_{a} + {x}_{b} + {x}_{c}}{3} , {G}_{y} = \frac{{y}_{1} + {y}_{2} + {y}_{3}}{3}$ where A, B, C are the three vertices of the triangle.

${G}_{x} = \frac{6 + 7 + 1}{3} = \frac{14}{3}$

${G}_{y} = \frac{3 + 4 + 2}{3} = 3$

Coordinates of centroid $G \left(\frac{14}{3} , 3\right)$

Coordinates of origin $O \left(0 , 0\right)$

Distance of centroid from origin is

$O G = \sqrt{{\left(\frac{14}{3}\right)}^{2} + {3}^{2}} = \textcolor{b l u e}{5.5478}$