Question

write co ordinates of the centroid of triangle passing through (3,-5),(4,3)and(11,-4)​

Answer 1

Given :

• A(3, -5)
• B(4, 3)
• C(11, -4)

To Find :

The centroid(G) of the triangle.

Solution :

Analysis :

We have to use the formula for centroid of a triangle.

Required Formula :

$\boxed{\bf(x, y) = \left(\dfrac{x_1+x_2+x_3}{2},\dfrac{y_1+y_2+y_3}{2}\right)}$

where,

• (x₁, y₁) = Coordinates of first point
• (x₂, y₂) = Coordinates of second point
• (x₃, y₃) = Coordinates of third point

Explanation :

Let the coordinates of the centroid be (x, y).

• A(3, -5)
• B(4, 3)
• C(11, -4)

Using the required formula,

$\bf(x, y) = \left(\dfrac{x_1+x_2+x_3}{2},\dfrac{y_1+y_2+y_3}{2}\right)$

where,

• x₁ = 3
• x₂ = 4
• x₃ = 11
• y₁ = -5
• y₂ = 3
• y₃ = -4

Substituting the values,

$\\ :\implies\sf(x, y) = \left(\dfrac{3+4+11}{2},\dfrac{(-5)+3+(-4)}{2}\right)$

$\\ :\implies\sf(x, y) = \left(\dfrac{18}{2},\dfrac{-5+3-4}{2}\right)$

$\\ :\implies\sf(x, y) = \left(\dfrac{18}{2},\dfrac{-9+3}{2}\right)$

$\\ :\implies\sf(x, y) = \left(\dfrac{18}{2},\dfrac{-6}{2}\right)$

$\\ :\implies\sf(x, y) = \left(\cancel{\dfrac{18}{2}},\cancel{\dfrac{-6}{2}}\right)$

$\\ :\implies\sf(x, y) = \left(9,-3\right)$

$\\ \therefore\boxed{\bf(x, y) = \left(9,-3\right).}$

Coordinates of the centroid of the triangle is G(9, -3).

Explore More :

Section Formula :

$\sf(x,y)=\left(\dfrac{m_1x_2+m_2x_1}{m_1+m_2},\dfrac{m_1y_2+m_2y_1}{m_1+m_2}\right)$

Mid-Point Formula :

$\sf(x, y) = \left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)$

where,

• (x₁, y₁) = Coordinates of first point
• (x₂, y₂) = Coordinates of second point
• m₁ : m₂ = the ratio