Answer: The required co-ordinates of the centroid are [tex]\left(-\dfrac{10}{3},2\right).[/tex]
Step-by-step explanation: We are to find the coordinates of the centroid of a triangle with vertices A(−6, 0) , B(−4, 4) , and C(0, 2).
We know that
the co-ordinates of the centroid of a triangle with vertices (a, b), (c, d) and (e, f) are given by
[tex]\left(\dfrac{a+c+e}{3},\dfrac{b+d+f}{3}\right).[/tex]
Therefore, the co-ordinates of the centroid of triangle ABC are
[tex]\left(\dfrac{-6+(-4)+0}{3},\dfrac{0+4+2}{3}\right)\\\\\\=\left(\dfrac{-10}{3},\dfrac{6}{3}\right)\\\\=\left(-\dfrac{10}{3},2\right).[/tex]
Thus, the required co-ordinates of the centroid are [tex]\left(-\dfrac{10}{3},2\right).[/tex]
