To find the centroid of triangle \( ABC \) with vertices \( A(2, 2) \), \( B(8, 2) \), and \( C(4, 7) \), you can use the formula for the centroid \( G \):
\[ G = \left( \frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3} \right) \]
where \( (x_1, y_1) \), \( (x_2, y_2) \), and \( (x_3, y_3) \) are the coordinates of vertices \( A \), \( B \), and \( C \) respectively.
Substituting the coordinates into the formula:
\[ G = \left( \frac{2 + 8 + 4}{3}, \frac{2 + 2 + 7}{3} \right) \]
Calculating the x-coordinate:
\[ \frac{2 + 8 + 4}{3} = \frac{14}{3} \]
Calculating the y-coordinate:
\[ \frac{2 + 2 + 7}{3} = \frac{11}{3} \]
Thus, the coordinates of the centroid \( G \) are:
\[ G = \left( \frac{14}{3}, \frac{11}{3} \right) \]
So the point of the centroid is:
\[ \text{centroid} = \left( \frac{14}{3}, \frac{11}{3} \right) \]
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