Question

Find the centroid of the triangle whose vertices are (-2,3),(2,-1) ,(4,0)​

Answer 1

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

$\green{\therefore{\text{Centroid(G)=}(\frac{4}{3},\frac{2}{3})}}$

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

$\green{ \underline \bold{Given : }} \\ : \implies \text{Coordinate \: of \: A = (-2,3)} \\ \\ : \implies \text{Coordinate \: of \: B = (2,-1)} \\ \\ : \implies \text{Coordinate \: of \: C = (4,0)} \\ \\ \red{ \underline \bold{To \: Find : }} \\ : \implies \text{Centroid(G) = ?}$

• According to given question :

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