# A triangle has corners at (2 ,9 ), (4 ,8 ), and (5 ,3 ). How far is the triangle's centroid from the origin?

Distance from centroid $= 7.6 \text{ }$units

#### Explanation:

Solve the centroid $C \left({x}_{c} , {y}_{c}\right)$ first

${x}_{c} = \frac{{x}_{1} + {x}_{2} + {x}_{3}}{3} = \frac{2 + 4 + 5}{3} = \frac{11}{3}$
${y}_{c} = \frac{{y}_{1} + {y}_{2} + {y}_{3}}{3} = \frac{9 + 8 + 3}{3} = \frac{20}{3}$

Solve distance $d$ from the origin using $\left({x}_{c} , {y}_{c}\right)$ and $\left(0 , 0\right)$

$d = \sqrt{{\left({x}_{c} - 0\right)}^{2} + {\left({y}_{c} - 0\right)}^{2}}$

$d = \sqrt{{\left(\frac{11}{3} - 0\right)}^{2} + {\left(\frac{20}{3} - 0\right)}^{2}}$

$d = 7.608474807 \text{ }$units