To find the centroid of triangle ABC, we can use the formula for the centroid (G) given the vertices coordinates A(x₁, y₁), B(x₂, y₂), and C(x₃, y₃):
\[ G\left(\frac{x₁ + x₂ + x₃}{3}, \frac{y₁ + y₂ + y₃}{3}\right) \]
Given the vertices:
- A(-3, -3)
- B(0, 6)
- C(4, -3)
We can substitute these coordinates into the centroid formula:
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Calculate the x-coordinate of the centroid: \[ G_x = \frac{-3 + 0 + 4}{3} = \frac{1}{3} \]
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Calculate the y-coordinate of the centroid: \[ G_y = \frac{-3 + 6 - 3}{3} = \frac{0}{3} = 0 \]
Putting it all together, the coordinates of the centroid G are: \[ G\left(\frac{1}{3}, 0\right) \]
Therefore, the centroid is located at:
\[ \left(\frac{1}{3}, 0\right) \]
From the provided responses, the correct answer is:
(13,0) (Note: this is likely a typo or misrepresentation. Based on the calculation, the centroid is \(\left(\frac{1}{3}, 0\right)\).