https://file.aiquickdraw.com/mathbot/file/17302117128216raprx57.jpg

To find the coordinates of the centroid \( G \) of triangle \( \triangle RST \), we can use the formula:

\[
G = \left( \frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3} \right)
\]

where \((x_1, y_1)\), \((x_2, y_2)\), and \((x_3, y_3)\) are the coordinates of the vertices \( R \), \( S \), and \( T \).

### Step 1: Identify the Coordinates
From the graph:
- \( R = (-6, 5) \)
- \( S = (4, 5) \)
- \( T = (1, -4) \)

### Step 2: Plug the Coordinates into the Centroid Formula
\[
G_x = \frac{-6 + 4 + 1}{3} = \frac{-1}{3} = -\frac{1}{3}
\]
\[
G_y = \frac{5 + 5 - 4}{3} = \frac{6}{3} = 2
\]

### Result
The coordinates of the centroid \( G \) are:
\[
G = \left( -\frac{1}{3}, 2 \right)
\]

Would you like further details or have any questions?

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Here are some related questions you might find interesting:
1. What is the centroid, and why is it located at this point?
2. How does the centroid divide each median in a triangle?
3. Can the centroid of a triangle ever lie outside the triangle?
4. How does the centroid relate to the balance point of a triangle?
5. What are the applications of centroids in real-world contexts?

**Tip:** The centroid divides each median in a triangle in a 2:1 ratio, with the centroid being closer to the midpoint of each side.

Find the coordinates of the centroid of triangle RST.

Learn how to find the centroid of triangle RST using coordinate geometry. This example uses the centroid formula to calculate the coordinates of point G, providing a step-by-step solution. Perfect for students in Grades 9-10.

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