To find the centroid of a triangle defined by the vertices \((-3, -1)\), \((2, -1)\), and \((2, 3)\), we use the formula for the centroid \((G_x, G_y)\):
\[ G_x = \frac{x_1 + x_2 + x_3}{3}, \quad G_y = \frac{y_1 + y_2 + y_3}{3} \]
Where:
- \((x_1, y_1) = (-3, -1)\)
- \((x_2, y_2) = (2, -1)\)
- \((x_3, y_3) = (2, 3)\)
Now we can calculate \(G_x\) and \(G_y\):
First, we calculate \(G_x\):
\[ G_x = \frac{-3 + 2 + 2}{3} = \frac{1}{3} \]
Next, we calculate \(G_y\):
\[ G_y = \frac{-1 + (-1) + 3}{3} = \frac{1}{3} \]
Thus, the coordinates of the centroid are:
\[ \text{centroid} \left( \frac{1}{3}, \frac{1}{3} \right) \]
Final answer:
\(\text{centroid} \left( \frac{1}{3}, \frac{1}{3} \right)\)
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