The coordinates of the centroid of the triangle STU is: (3, 1).
Recall:
- The centroid of a triangle is the point of concurrency of all the medians of a triangle.
- The centroid of triangle ABC that is shown in the image attached below is point G.
- The formula for finding the coordinate of the centroid of a triangle is: [tex]\mathbf{(x, y) = (\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3})}[/tex]
Thus, given the vertices of a triangle as: S(5, 5), T(11, -3), U(-1, 1)
[tex]S(5, 5) = (x_1, y_1)\\\\T(11, -3) = (x_2, y_2)\\\\U(-1, 1) = (x_3, y_3)[/tex]
[tex](x, y) = (\frac{5 + 11 +(-1)}{3}, \frac{5 + (-3) + 1}{3})\\\\(x, y) = (\frac{15}{3}, \frac{3}{3})\\\\\mathbf{(x, y) = (3, 1)}[/tex]
Therefore, the coordinates of the centroid of the triangle STU is: (3, 1).
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