Answer:
Therefore, the coordinates of the centroid of a triangle is
[tex]G(x,y)=(2,1)[/tex]
Step-by-step 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
[tex]G(x,y)=(\dfrac{x_{1}+x_{2}+x_{3}}{3},\dfrac{y_{1}+y_{2}+y_{3}}{3})[/tex]
Substituting the values we get
[tex]G(x,y)=(\dfrac{3+5+-2}{3},\dfrac{3+-1+1}{3})[/tex]
[tex]G(x,y)=(\dfrac{6}{3},\dfrac{3}{3})=(2,1)[/tex]
Therefore, the coordinates of the centroid of a triangle is
[tex]G(x,y)=(2,1)[/tex]
