To find the centroid of triangle ABC, we can use the formula for the centroid \(G\) of a triangle with vertices at \((x_1, y_1)\), \((x_2, y_2)\), and \((x_3, y_3)\):
\[ G = \left( \frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3} \right) \]
For triangle ABC, the vertices are:
- \(A(-3, -3)\)
- \(B(0, 6)\)
- \(C(4, -3)\)
Now we can plug in these coordinates into the centroid formula.
First, calculate the x-coordinate of the centroid:
\[ x_G = \frac{-3 + 0 + 4}{3} = \frac{1}{3} \]
Next, calculate the y-coordinate of the centroid:
\[ y_G = \frac{-3 + 6 + (-3)}{3} = \frac{0}{3} = 0 \]
Thus, the centroid \(G\) of triangle ABC is:
\[ G = \left( \frac{1}{3}, 0 \right) \]
This means that the centroid and, therefore, the point where the medians of triangle ABC meet is \(\left( \frac{1}{3}, 0 \right)\).
The correct answer is:
A. \(\left( \frac{1}{3}, 0 \right)\).