Question

the centroid of triangle made by the vertices A(-2,3) ; B(4,1) ; C(1,2) is​

Answer 1

Answer:-

Given:

Vertices of a triangle are A( - 2 , 3) , B (4 , 1) , C (1 , 2).

Let the co - ordinates of the centroid be (x , y)

We know that,

Centroid of a triangle with vertices (x₁ , y₁) (x₂ , y₂) & (x₃ , y₃) is :

$\boxed {\large {\sf \: G(x \: , \: y) = \bigg( \dfrac{x_1 + x_2 + x_3}{3} \: \: , \: \: \dfrac{y_1 + y_2 + y_3}{3} \bigg)}}$

Let,

• x₁ = - 2

• x₂ = 4

• x₃ = 1

• y₁ = 3

• y₂ = 1

• y₃ = 2

Hence,

$\implies \sf \:G (x \: , \: y) = \bigg( \frac{ - 2 + 4 + 1}{3} \: \: ,\: \: \frac{3 + 1 + 2}{2} \bigg) \\ \\ \\ \implies \sf \:G (x \: , \: y) = \bigg( \frac{3}{3} \: \: , \: \: \frac{6}{3} \bigg) \\ \\ \\ \implies \boxed{\sf \:G (x \: , \: y) = (1 \: , \: 2)}$

∴ The centroid of the given triangle is (1 , 2).

Answer 2

Answer:

Given :

• the vertices A(-2,3) ; B(4,1) ; C(1,2)

To Find :

• vertices A(-2,3) ; B(4,1) ; C(1,2) is

Solution :

A ( - 2, 3 ) = A ( x1, y1 )

where, x1 = - 2, y1 = 3

B ( 4, 1 ) = B ( x2, y2 )

where, x2 = 4, y2 = 1

C ( 1, 2 ) = C ( x3, y3 )

where, x3 = 1, y3 = 2

Centroid of triangle formula,

= ( x1 + x2 + x3,    y1 + y2 + y3 )

 ___________ , __________

             3                       3

Substitute all Values :

= ( - 2 + 4 + 1  3 + 1 + 2 )

  ________ , _______

          3                 3

= ( 3 / 3 , 6 / 3 )

= ( 1, 2 )

Therefore, the centroid of triangle made by the vertices A ( - 2 , 3 ) ; B ( 4 , 1 ) ; C ( 1 , 2 ) is ( 1, 2 )