Find the point of intersection of the medians of a triangle whose vertices are :
`(-1,0)` , `(5,-2)` and `(8,2)`.

Answer

To find the point of intersection of the medians of a triangle (the centroid), we can use the formula for the centroid given the vertices of the triangle.

### Step-by-Step Solution:

1. **Identify the vertices of the triangle:**
The vertices of the triangle are given as:
- \( A(-1, 0) \)
- \( B(5, -2) \)
- \( C(8, 2) \)

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

3. **Substitute the coordinates into the formula:**
Here, substituting the coordinates of the vertices into the formula:
- \( x_1 = -1 \), \( y_1 = 0 \)
- \( x_2 = 5 \), \( y_2 = -2 \)
- \( x_3 = 8 \), \( y_3 = 2 \)

The x-coordinate of the centroid \( G_x \) is calculated as:
\[ G_x = \frac{-1 + 5 + 8}{3} \]
The y-coordinate of the centroid \( G_y \) is calculated as:
\[ G_y = \frac{0 - 2 + 2}{3} \]

4. **Calculate the x-coordinate:**
\[ G_x = \frac{-1 + 5 + 8}{3} = \frac{12}{3} = 4 \]

5. **Calculate the y-coordinate:**
\[ G_y = \frac{0 - 2 + 2}{3} = \frac{0}{3} = 0 \]

6. **Combine the coordinates to find the centroid:**
Thus, the point of intersection of the medians, or the centroid \( G \), is:
\[ G(4, 0) \]

### Final Answer:
The point of intersection of the medians of the triangle is \( (4, 0) \).