Triangle ABC

To find the centroid of triangle ABC, we can apply the formula for the coordinates of the centroid (G). The centroid of a triangle with vertices \(A(x_1, y_1)\), \(B(x_2, y_2)\), and \(C(x_3, y_3)\) is given by:

\[
G = \left( \frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3} \right)
\]

Given the vertices:
- \(A(-2, -3)\)
- \(B(4, 0)\)
- \(C(-2, 2)\)

We can calculate the x-coordinate of the centroid:

\[
x_G = \frac{-2 + 4 - 2}{3} = \frac{0}{3} = 0
\]

Now, we calculate the y-coordinate of the centroid:

\[
y_G = \frac{-3 + 0 + 2}{3} = \frac{-1}{3}
\]

So the coordinates of the centroid \(G\) are:

\[
G = \left( 0, -\frac{1}{3} \right)
\]

Thus, the centroid of triangle ABC is \((0, -\frac{1}{3})\).

Among the given options, the correct response is:

**open paren 0 comma negative 1 third close paren**.