So, let's find the coordinates of the centroid first.
We can calculate the centroid of the triangle by taking the average of the x coordinates and the y coordinates of all the three vertices. So, the centroid formula can be mathematically expressed as:
[tex]C(x,y)=(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3_{}}{3})[/tex]So, if we replace:
[tex]\begin{gathered} C(x,y)=(\frac{-4+2+8}{3},\frac{0+8+0}{3}) \\ \\ C(x,y)=(\frac{6}{3},\frac{8}{3}) \\ \\ C(x,y)=(2,\frac{8}{3})\to C(x,y)=(2,2\frac{2}{3}) \end{gathered}[/tex]Therefore, the centroid has coordinates (2, 2 2/3).