To find the centroid of a triangle, you can use the formula for the centroid, which is the average of the coordinates of the vertices of the triangle. If the vertices of the triangle are given as A(x₁, y₁), B(x₂, y₂), and C(x₃, y₃), then the coordinates of the centroid (G) can be calculated using:
\[ G\left(x_G, y_G\right) = \left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) \]
However, based on the response options you've provided, it seems like you are looking for a specific one that represents the centroid of a certain triangle.
If you want to check the answers based on the vertices of the triangle that you might have in the image, please provide the coordinates of those vertices, and we can calculate the centroid together.
Based on the responses given, if we assume the vertices lead to one of those points, based on typical locations, I would suggest checking them in terms of how they relate to a triangle's average point (with their coordinates).
Given the options:
- (−1, 1)
- (−3, 1)
- (−13, 13)
- \(\left(-\frac{1}{3}, \frac{1}{3}\right)\)
- \(\left(-\frac{1}{2}, \frac{1}{2}\right)\)
If more information was provided about the vertices, we would be able to calculate and confirm which option corresponds to the centroid. In lieu of that, if any of those coordinates seem plausible based on typical triangle setups, you may choose the one that looks most reasonable.
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