A(-1, 3), B(4, 2) and C(3, -2) are the vertices of a triangle.
Find the coordinates of the centroid G of the triangle.

Answer

To find the coordinates of the centroid \( G \) of the triangle with vertices \( A(-1, 3) \), \( B(4, 2) \), and \( C(3, -2) \), we can use the formula for the centroid of a triangle. The coordinates of the centroid \( G(x, y) \) are given by:

\[ G_x = \frac{x_1 + x_2 + x_3}{3} \]
\[ G_y = \frac{y_1 + y_2 + y_3}{3} \]

where \( (x_1, y_1) \), \( (x_2, y_2) \), and \( (x_3, y_3) \) are the coordinates of the vertices \( A \), \( B \), and \( C \).

### Step 1: Identify the coordinates of the vertices
The coordinates of the vertices are:
- \( A(-1, 3) \)
- \( B(4, 2) \)
- \( C(3, -2) \)

### Step 2: Calculate the x-coordinate of the centroid
Using the formula for \( G_x \):
\[ G_x = \frac{x_A + x_B + x_C}{3} = \frac{-1 + 4 + 3}{3} \]
Calculating the sum:
\[ G_x = \frac{6}{3} = 2 \]

### Step 3: Calculate the y-coordinate of the centroid
Using the formula for \( G_y \):
\[ G_y = \frac{y_A + y_B + y_C}{3} = \frac{3 + 2 - 2}{3} \]
Calculating the sum:
\[ G_y = \frac{3}{3} = 1 \]

### Step 4: Write the coordinates of the centroid
Thus, the coordinates of the centroid \( G \) are:
\[ G(2, 1) \]

### Final Answer:
The coordinates of the centroid \( G \) of the triangle are \( (2, 1) \).