# A triangle has corners at (1 ,2 ), (9 ,6 ), and (4 ,5 ). How far is the triangle's centroid from the origin?

Jan 31, 2017

"the centroid of triangle located at :"color(red)(Centroid(4.67,4.33)
$\text{length from origin is : "6.37" units}$

#### Explanation:

$\text{Strategy :}$
$\diamond \text{ find the centroid of triangle}$coordinates(x,y)
$\diamond \text{ find length between origin and centroid}$

$\text{The coordinates of Centroid "color(red)( Centroid(x,y))" can be calculated using :}$

$x = \frac{{x}_{1} + {x}_{2} + {x}_{3}}{3}$

$y = \frac{{y}_{1} + {y}_{2} + {y}_{3}}{3}$

$x = \frac{1 + 9 + 4}{3} = \frac{14}{3} = 4.67$

$y = \frac{2 + 6 + 5}{3} = \frac{13}{3} = 4.33$

$\text{The Centroid located :} \textcolor{red}{C e n t r o i d \left(4.67 , 4.33\right)}$
$\text{............................................................................................}$
$\text{length between O(0,0) and } \textcolor{red}{C e n t r o i d \left(4.67 , 4.33\right)}$

$d = \sqrt{{\left(4.33 - 0\right)}^{2} + {\left(4.67 - 0\right)}^{2}}$

$d = \sqrt{{\left(4.33\right)}^{2} + {\left(4.67\right)}^{2}}$

$d = 6.37 \text{ units}$