A triangle has corners at (4 ,7 ), (2 ,3 ), and (5 ,8 ). How far is the triangle's centroid from the origin?

Jun 10, 2017

The distance is $= 7.03$

Explanation:

The centroid of the triangle is

$\left(\frac{{x}_{1} + {x}_{2} + {x}_{3}}{3} , \frac{{y}_{1} + {y}_{2} + {y}_{3}}{3}\right)$

$= \left(\frac{4 + 2 + 5}{3} , \frac{7 + 3 + 8}{3}\right)$

$= \left(\frac{11}{3} , 6\right)$

The distance of the centroid frm the origin is

$= \sqrt{{\left(\frac{11}{3}\right)}^{2} + {\left(6\right)}^{2}}$

$= 7.03$
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