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;

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

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;

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

ANSWER:

The coordinates of the centroid therefore is;

$(-\frac{10}{3},2)$