# A triangle has corners at (7 ,2 ), (4 ,3 ), and (5 ,1 ). How far is the triangle's centroid from the origin?

Dec 4, 2017

$5.70 u n i t s$

#### Explanation:

Find the centroid of the triangle

For Co-ordinates $\left(X 1 , Y 1\right) , \left(X 2 , Y 2\right) , \left(X 3 , Y 3\right)$

Use formula $c e n t r o i d \left(x , y\right) = \left(\frac{X 1 + X 2 + X 3}{3} , \frac{Y 1 , Y 2 , Y 3}{3}\right)$

Therefore substitute the Co-ordinates and the centroid Co-ordinate would be $\left(\frac{16}{3} , 2\right)$

Find distance from origin to the centroid by using pythagoras:

$D i s \tan c e = \sqrt{{\left(\frac{16}{3}\right)}^{2} + {2}^{2}}$

$D i s \tan c e = 5.70 u n i t s$