Question

find centroid of triangle who's vertics are (4,6)(2,-2)(0,2)

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Answer 1

$\begin{gathered} \green{ \underline \bold{Given : }} \\ : \implies \text{Coordinate \: of \: A = (4,6)} \\ \\ : \implies \text{Coordinate \: of \: B = (2,-2)} \\ \\ : \implies \text{Coordinate \: of \: C = (0,2)} \\ \\ \red{ \underline \bold{To \: Find : }} \\ : \implies \text{Centroid(G) = ?}\end{gathered}$

• According to given question :

$\begin{gathered} \bold{As \: we \: know \: that} \\ \circ \: \text{Centroid \: of \: triangle(G}) \\ \\ \circ \: \text{For \: x }= \frac{ x_{1} + x_{2} + x_{3} }{3} \\ \\ \circ \: \text{For \: y} = \frac{ y_{1} + y_{2} + y_{3} }{3} \\ \\ \text{Let \: Coordinate \: of \: (g) =( x,y) } \\ \\ \bold{For \: x}\\ : \implies x = \frac{ x_{1} + x_{2} + x_{3} }{3} \\ \\ : \implies x = \frac{ 4 +2 + 0}{3} \\ \\ : \implies x = \frac{6}{3} \\ \\ \green{: \implies x =2} \\ \\ \bold{For \: y}\\ : \implies y= \frac{ y_{1} + y_{2} + y_{3} }{3} \\ \\ : \implies y= \frac{ 6 +(-2)+2}{3} \\ \\ : \implies y = \frac{6}{3} \\ \\ \green{: \implies y =2} \\ \\ \green{\therefore \text{Coordinate \: of \: centroid(G) = }(2,2)}\end{gathered}$