Question

What are the coordinates of the centroid of a triangle with vertices A(−3, 1) , B(1, 6) , and C(5, 2) ? Enter your answer by filling in the boxes.

Answer 1

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}`

You can use the following formula to find the x-coordinate of the Centroid:

`O_x=(A_x+B_x+C_x)/(3)`

And this formula to find the y-coordinate of the Centroid:

`O_y=(A_y+B_y+C_y)/(3)`

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}`

Therefore, substituting values into the formulas and evaluating, you get:

`O_x=\frac{-3_{}+1+5}{3}=(3)/(3)=1`
`O_y=(1+6+2)/(3)=(9)/(3)=3`

Hence, the answer is:

`Centroid=\mleft(1,3\mright)`