Question

find the centroid of the triangle ABC whose vertices are A(-2,0) B(7,-3))and C(6,2)

Answer 1

Answer:

Step-by-step explanation:

Centroid of a triangle can be found by the formula as follows:

Assuming Centroid to be ( x,y ) we get,

⇒ x = ( x₁ + x₂ + x₃ ) / 3 ; y = ( y₁ + y₂ + y₃ ) / 3

According to the question,

x₁ = -2, x₂ = 7, x₃ = 6 and y₁ = 0, y₂ = -3, y₃ = 2

Applying the values in formula we get,

⇒ x = ( -2 + 7 + 6 ) / 3

⇒ x = ( 11 / 3 )

⇒ y = ( 0 - 3 + 2 ) / 3

⇒ y = -1 / 3

Hence the centroid coordinates are ( 11/3 , -1,3 )

Thanks !!

Answer 2

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

$\green{\therefore{\text{Centroid(G)=}(\frac{11}{3},\frac{-1}{3})}}$

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

$\green{ \underline \bold{Given : }} \\ : \implies \text{Coordinate \: of \: A = (-2,0)} \\ \\ : \implies \text{Coordinate \: of \: B = (7,-3)} \\ \\ : \implies \text{Coordinate \: of \: C = (6,2)} \\ \\ \red{ \underline \bold{To \: Find : }} \\ : \implies \text{Centroid(G) = ?}$

• According to given question :

$\bold{As \: we \: know \: that} \\ \circ \: \text{Centroid \: of \: triangle(G}) \\ \\ \circ \: \text{For \: x }= \frac{ x_{1} + x_{2} + x_{3} }{3} \\ \\ \circ \: \text{For \: y} = \frac{ y_{1} + y_{2} + y_{3} }{3} \\ \\ \text{Let \: Coordinate \: of \: (g) =( x,y) } \\ \\ \bold{For \: x}\\ : \implies x = \frac{ x_{1} + x_{2} + x_{3} }{3} \\ \\ : \implies x = \frac{-2+7 +6}{3} \\ \\ : \implies x = \frac{13-2}{3} \\ \\ \green{: \implies x =\frac{11}{3}} \\ \\ \bold{For \: y}\\ : \implies y= \frac{ y_{1} + y_{2} + y_{3} }{3} \\ \\ : \implies y= \frac{ 0 +(-3)+2}{3} \\ \\ : \implies y = \frac{2-3}{3} \\ \\ \green{: \implies y =\frac{-1}{3}} \\ \\ \green{\therefore \text{Coordinate \: of \: centroid(G) = }(\frac{11}{3},\frac{-1}{3})}$