Question

find the centroid of triangle ABC whose vertices , are A(2,-3) B(4,2) and C(-3,-2)

Answer 1

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Answer 2

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\therefore{\text{Centroid(G)=}(1,-1)}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{ \underline \bold{Given : }} \\ : \implies \text{Coordinate \: of \: A = (2,-3)} \\ \\ : \implies \text{Coordinate \: of \: B = (4,2)} \\ \\ : \implies \text{Coordinate \: of \: C = (-3,-2)} \\ \\ \red{ \underline \bold{To \: Find : }} \\ : \implies \text{Centroid(G) = ?}$

• According to given question :

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