Question

What are the coordinates of the centroid of a triangle with vertices (-6,0), (-4,4), and (0,2)?

Answer 1

Given a triangle with the following coordinates;

`(-6,0),(-4,4),(0,2)`

The centroid of the triangle can be found at the following coordinates;

`\begin{gathered} ((x_1+x_2+x_3))/(3),((y_1+y_2+y_3))/(3) \\ \end{gathered}`

Where the three vertices are;

`\begin{gathered} A(x_1,y_1)=(-6,0) \\ B(x_2,y_2)=(-4,4) \\ C(x_3,y_3)=(0,2) \end{gathered}`

We now have the centroid as follows;

`\begin{gathered} ((-6+\lbrack-4\rbrack+0))/(3),((0+4+2))/(3) \\ ((-6-4+0))/(3),(6)/(3) \\ -(10)/(3),2 \end{gathered}`

ANSWER:

The coordinates of the centroid therefore is;

`(-(10)/(3),2)`