Given the vertices of the triangle ABC:
![\begin{gathered} A\mleft(-3,1\mright) \\ B\mleft(1,6\mright) \\ C\mleft(5,2\mright) \end{gathered}](https://img.qammunity.org/qa-images/2023/formulas/mathematics/college/pa7u41ptb6pkh8jz5dh7.png)
You can use the following formula to find the x-coordinate of the Centroid:
![O_x=(A_x+B_x+C_x)/(3)](https://img.qammunity.org/qa-images/2023/formulas/mathematics/college/xdxoh6alxgxvejgsoyu0.png)
And this formula to find the y-coordinate of the Centroid:
![O_y=(A_y+B_y+C_y)/(3)](https://img.qammunity.org/qa-images/2023/formulas/mathematics/college/dwe269j0wx1eexpddkdg.png)
In this case, you know that:
![\begin{gathered} A_x=-3 \\ B_x=1 \\ C_x=5 \\ \\ A_y=1 \\ B_y=6 \\ C_y=2 \end{gathered}](https://img.qammunity.org/qa-images/2023/formulas/mathematics/college/lx61pr8io80ceyoyfpgt.png)
Therefore, substituting values into the formulas and evaluating, you get:
![O_x=\frac{-3_{}+1+5}{3}=(3)/(3)=1](https://img.qammunity.org/qa-images/2023/formulas/mathematics/college/7g626kpncmvvzq6wetzw.png)
![O_y=(1+6+2)/(3)=(9)/(3)=3](https://img.qammunity.org/qa-images/2023/formulas/mathematics/college/rvnnj8fhaeooiauve8za.png)
Hence, the answer is:
![Centroid=\mleft(1,3\mright)](https://img.qammunity.org/qa-images/2023/formulas/mathematics/college/3fsmecdk82p587tsfh9j.png)