Answer:
Centroid of a Triangle states that the centre of the triangle that can be calculated as the point of intersection of all the three medians of a triangle, and this median is a line drawn from the midpoint of a side to the opposite vertex.
The coordinates of the centroid are simply the average of the coordinates of the vertices of triangle ABC.
The Centroid formula is,
[tex]C = {\frac{x_{1}+x_{2}+x_{3}}{3} , \frac{y_{1}+y_{2}+y_{3}}{3}[/tex] where C is the centroid of the triangle ; [tex]x_{1},x_{2},x_{3}[/tex] are the x-coordinates of the vertices of the triangle and [tex]y_{1},y_{2},y_{3}[/tex] are the y-coordinates of the vertices of the triangle.
Given the vertices of triangle A([tex]x_{1},y_{1}[/tex])= (-6,0) , B([tex]x_{2},y_{2}[/tex])= (-4, 4) and C([tex]x_{3},y_{3}[/tex])=(0,2)
then,
the centroid of triangle C is,
[tex]\{\frac{-6+(-4)+0}{3} , \frac{0+4+2}{3}\}[/tex] = [tex]\{\frac{-6-4+0}{3} , \frac{6}{3}\}=\{\frac{-10}{3} , 2\}[/tex]
