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

Sep 11, 2016

The centroid coordinates are the average of the coordinates of the vertices; then use the distance formula.

#### Explanation:

The coordinates of the centroid are the average of the x and y coordinates of the vertices (corners).

Vertices: $\left(4 , 6\right)$, $\left(3 , 3\right)$, $\left(6 , 5\right)$

x coordinate of centroid:
$\frac{4 + 3 + 6}{2} = \frac{13}{2}$

y coordinate of the centroid:
$\frac{6 + 3 + 5}{2} = 7$

Centroid is located at $\left(\frac{13}{2} , 7\right)$

To find the distance from the origin $\left(0 , 0\right)$, use the distance formula.

$\sqrt{{\left(\frac{13}{2} - 0\right)}^{2} + {\left(7 - 0\right)}^{2}}$

$\sqrt{\frac{169}{4} + 49}$

$\sqrt{\frac{365}{4}}$

$\frac{\sqrt{365}}{2}$