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

Mar 21, 2017

$\text{Answer l="10/3sqrt 2=4.7" } u n i t s .$

Explanation:

$\text{Let P(x,y) be triangle's centroid .}$

"The coordinates of centroid can be calculated the formula" $\text{given below.}$

$P \left(x , y\right) = \left(\frac{{x}_{A} + {x}_{B} + {x}_{C}}{3} , \frac{{y}_{A} + {y}_{B} + {y}_{C}}{3}\right)$

$P \left(x , y\right) = \left(\frac{1 + 3 + 6}{3} , \frac{4 + 4 + 2}{3}\right)$

$P \left(x , y\right) = \left(\frac{10}{3} , \frac{10}{3}\right)$

$\text{Distance from The point O(0,0) :}$

$l = \sqrt{{\left(\frac{10}{3}\right)}^{2} + {\left(\frac{10}{3}\right)}^{2}}$

$l = \sqrt{\frac{100}{9} + \frac{100}{9}}$

$l = \sqrt{\frac{2 \cdot 100}{9}}$

$l = \frac{10}{3} \sqrt{2} = 4.7$