The centroid of the triangle formed by (7, 4), (4, -6), (-5, 2) is

Answer

To find the centroid of the triangle formed by the points (7, 4), (4, -6), and (-5, 2), we can use the formula for the centroid of a triangle in a coordinate system. The centroid (G) is given by the coordinates:

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

where \((x_1, y_1)\), \((x_2, y_2)\), and \((x_3, y_3)\) are the vertices of the triangle.

### Step-by-step Solution:

1. **Identify the coordinates of the vertices**:
- Let \((x_1, y_1) = (7, 4)\)
- Let \((x_2, y_2) = (4, -6)\)
- Let \((x_3, y_3) = (-5, 2)\)

2. **Calculate the x-coordinate of the centroid**:
\[ x_G = \frac{x_1 + x_2 + x_3}{3} = \frac{7 + 4 - 5}{3} \]
\[ x_G = \frac{6}{3} = 2 \]

3. **Calculate the y-coordinate of the centroid**:
\[ y_G = \frac{y_1 + y_2 + y_3}{3} = \frac{4 - 6 + 2}{3} \]
\[ y_G = \frac{0}{3} = 0 \]

4. **Write the coordinates of the centroid**:
The centroid of the triangle is \(G(2, 0)\).

### Final Answer:
The centroid of the triangle formed by the points (7, 4), (4, -6), and (-5, 2) is \(G(2, 0)\).