Given the vertices of the triangle ABC:
[tex]\begin{gathered} A\mleft(-3,1\mright) \\ B\mleft(1,6\mright) \\ C\mleft(5,2\mright) \end{gathered}[/tex]You can use the following formula to find the x-coordinate of the Centroid:
[tex]O_x=\frac{A_x+B_x+C_x}{3}[/tex]And this formula to find the y-coordinate of the Centroid:
[tex]O_y=\frac{A_y+B_y+C_y}{3}[/tex]In this case, you know that:
[tex]\begin{gathered} A_x=-3 \\ B_x=1 \\ C_x=5 \\ \\ A_y=1 \\ B_y=6 \\ C_y=2 \end{gathered}[/tex]Therefore, substituting values into the formulas and evaluating, you get:
[tex]O_x=\frac{-3_{}+1+5}{3}=\frac{3}{3}=1[/tex][tex]O_y=\frac{1+6+2}{3}=\frac{9}{3}=3[/tex]Hence, the answer is:
[tex]Centroid=\mleft(1,3\mright)[/tex]
