To find the centroid of triangle ABC, we need to use the formula for the centroid, which is the average of the coordinates of its vertices. The centroid \( G \) is given by:
\[ G\left( \frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3} \right) \]
Assuming the coordinates of points A, B, and C are \((x_1, y_1)\), \((x_2, y_2)\), and \((x_3, y_3)\), let's calculate the centroid step by step.
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Identify the coordinates of the vertices: You mentioned there are coordinates for points A, B, and C, but did not specify them. For the sake of illustration, let's say:
- Point A: \( (x_1, y_1) \)
- Point B: \( (x_2, y_2) \)
- Point C: \( (x_3, y_3) \)
For determining the centroid exactly, you'll need to replace these hypothetical coordinates with the actual coordinates from the image you referenced.
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Calculate the centroid:
- Substitute the actual coordinates into the formula:
\[ G\left( \frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3} \right) \]
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Provide the final answer:
- Check the resulting coordinates against the options you provided.
If you can provide the actual coordinates for points A, B, and C, I can help you with the exact calculation, or you can proceed with the steps above to find the centroid and match it with the choices:
- \( \left( \frac{8}{3}, 2 \right) \)
- \( \left( \frac{10}{3}, 0 \right) \)
- \( (3, 2) \)
- \( \left( \frac{38}{2}, 2 \right) \)
Just plug in the numbers from the vertices and you’ll find which option corresponds to the computed centroid.