To find the centroid of triangle ABC, we can use the formula for the centroid (G) of a triangle with vertices A(x₁, y₁), B(x₂, y₂), and C(x₃, y₃):
\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) \]
Given the vertices of triangle ABC:
- A(-2, -3)
- B(4, 0)
- C(-2, 2)
Let's substitute these coordinates into the centroid formula.
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Calculate the x-coordinate: \[ \frac{-2 + 4 - 2}{3} = \frac{0}{3} = 0 \]
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Calculate the y-coordinate: \[ \frac{-3 + 0 + 2}{3} = \frac{-1}{3} \]
Thus, the coordinates of the centroid G are: \[ G\left(0, -\frac{1}{3}\right) \]
So the centroid of triangle ABC is \((0, -\frac{1}{3})\).
Among the provided responses, the correct one is:
(0, -1/3) or (0, -\frac{1}{3}).