Question

The coordinatinates of the centroid of a triangle with the given vertices 3,3 5,-1 -2,1​

Answer 1

Therefore, the coordinates of the centroid of a triangle is

`G(x,y)=(2,1)`

Explanation:

Given:

Let,

point A( x₁ , y₁) ≡ ( 3, 3)

point B( x₂ , y₂) ≡ (5 , -1)

point C( x₃ , y₃) ≡ (-2 , 1)

To Find:

Centroid, G (x,y) = ? (say)

Solution:

Centroid:

Centroid is a point where all the three medians of the triangle intersect.

It is denoted as G and the coordinates are give by

`G(x,y)=((x_(1)+x_(2)+x_(3))/(3),(y_(1)+y_(2)+y_(3))/(3))`

Substituting the values we get

`G(x,y)=((3+5+-2)/(3),(3+-1+1)/(3))`

`G(x,y)=((6)/(3),(3)/(3))=(2,1)`

Therefore, the coordinates of the centroid of a triangle is

`G(x,y)=(2,1)`