The centroid of `DeltaABC` , where `A(-4 , 6)` , B (2, -2) and C(2,5) is :

Options

A. (0,2)
B. (0,3)
C. (1,3)
D. (1,2)

Answer

To find the centroid of triangle ABC with vertices A(-4, 6), B(2, -2), and C(2, 5), we can use the formula for the centroid (G) of a triangle given by the coordinates of its vertices.

### Step-by-Step Solution:

1. **Identify the coordinates of the vertices:**
- A = (x1, y1) = (-4, 6)
- B = (x2, y2) = (2, -2)
- C = (x3, y3) = (2, 5)

2. **Use the centroid formula:**
The coordinates of the centroid (G) are given by:
\[ G(x, y) = \left( \frac{x1 + x2 + x3}{3}, \frac{y1 + y2 + y3}{3} \right) \]

3. **Calculate the x-coordinate of the centroid:**
\[ x = \frac{-4 + 2 + 2}{3} \]
Simplifying this:
\[ x = \frac{0}{3} = 0 \]

4. **Calculate the y-coordinate of the centroid:**
\[ y = \frac{6 + (-2) + 5}{3} \]
Simplifying this:
\[ y = \frac{6 - 2 + 5}{3} = \frac{9}{3} = 3 \]

5. **Combine the x and y coordinates to find the centroid:**
Thus, the coordinates of the centroid G are:
\[ G(0, 3) \]

### Final Answer:
The centroid of triangle ABC is \( G(0, 3) \).