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

Jul 25, 2016

distance of centroid from origin is: $\text{ } \frac{11}{3} \sqrt{2}$

#### Explanation:

$\textcolor{b l u e}{\text{Determine the Centroid - Shortcut method}}$

The triangle's centroid is the mean point.

So mean $x \text{ is } \frac{1 + 3 + 7}{3} = \frac{11}{3} \to 3 \frac{2}{3}$

Mean $y \text{ is } \frac{2 + 4 + 5}{3} = \frac{11}{3} \to 3 \frac{2}{3}$

$\textcolor{b l u e}{\text{Centroid} \to \left(x , y\right) = \left(\frac{11}{3} , \frac{11}{3}\right)}$
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$\textcolor{w h i t e}{.}$

$\textcolor{b l u e}{\text{Determine distance of centroid from origin}}$

Using Pythagoras

$\text{distance (d)" = sqrt(2(11/3)^2)" "=" } \frac{11}{3} \sqrt{2}$

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$\textcolor{b r o w n}{\text{If you so chose you could check this by building}}$
$\textcolor{b r o w n}{\text{equations of lines and solving for simultaneous equations}}$