Question

find the centroid of the triangle whose vertices are(-4,6)(2-2)and(2,5)

Answer 1

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

$\green{\therefore{\text{Centroid(G)=}(0,3)}}$

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

$\green{ \underline \bold{Given : }} \\ : \implies \text{Coordinate \: of \: A = (-4,6)} \\ \\ : \implies \text{Coordinate \: of \: B = (2,-2)} \\ \\ : \implies \text{Coordinate \: of \: C = (2,5)} \\ \\ \red{ \underline \bold{To \: Find : }} \\ : \implies \text{Centroid(G) = ?}$

• According to given question :

$\bold{As \: we \: know \: that} \\ \circ \: \text{Centroid \: of \: triangle(G}) \\ \\ \circ \: \text{For \: x }= \frac{ x_{1} + x_{2} + x_{3} }{3} \\ \\ \circ \: \text{For \: y} = \frac{ y_{1} + y_{2} + y_{3} }{3} \\ \\ \text{Let \: Coordinate \: of \: (g) =( x,y) } \\ \\ \bold{For \: x}\\ : \implies x = \frac{ x_{1} + x_{2} + x_{3} }{3} \\ \\ : \implies x = \frac{ -4 +2 + 2}{3} \\ \\ : \implies x = \frac{-4+4}{3} \\ \\ \green{: \implies x =0} \\ \\ \bold{For \: y}\\ : \implies y= \frac{ y_{1} + y_{2} + y_{3} }{3} \\ \\ : \implies y= \frac{ 6 +(-2)+5}{3} \\ \\ : \implies y = \frac{11-2}{3} \\ \\ \green{: \implies y =3} \\ \\ \green{\therefore \text{Coordinate \: of \: centroid(G) = }(0,3)}$