If the vertices of a `DeltaABC` are A(-1,0), B(5,-2) and C(8,2). Then its centrid is :

Options

A. (4,0)
B. (6,0)
C. (12,0)
D. (0,6)

Answer

To find the centroid of triangle ABC with vertices A(-1, 0), B(5, -2), and C(8, 2), we can use the formula for the centroid of a triangle. The centroid (G) can be calculated using the coordinates of the vertices as follows:

### Step-by-Step Solution:

1. **Identify the Coordinates of the Vertices:**
- A = (-1, 0)
- B = (5, -2)
- C = (8, 2)

2. **Use the Centroid Formula:**
The formula for the centroid (G) of a triangle with vertices (x1, y1), (x2, y2), and (x3, y3) is:
\[ G\left( \frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3} \right) \]

3. **Calculate the x-coordinate of the Centroid:**
\[ x_G = \frac{x_1 + x_2 + x_3}{3} = \frac{-1 + 5 + 8}{3} \]
\[ x_G = \frac{12}{3} = 4 \]

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

5. **Combine the Coordinates:**
Thus, the coordinates of the centroid G are:
\[ G(4, 0) \]

### Final Answer:
The centroid of triangle ABC is at the point **(4, 0)**.