Find the co-ordinates of the point of intersection of the medians of triangle ABC, given A = (-2, 3), B = (6, 7) and C = (4,1).

Answer

To find the coordinates of the point of intersection of the medians of triangle ABC, we will calculate the centroid of the triangle using the given vertices A, B, and C.

### Step-by-Step Solution:

1. **Identify the Coordinates of the Vertices:**
- A = (-2, 3)
- B = (6, 7)
- C = (4, 1)

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

3. **Calculate the x-coordinate of the Centroid:**
\[ G_x = \frac{x_1 + x_2 + x_3}{3} = \frac{-2 + 6 + 4}{3} \]
Simplifying this:
\[ G_x = \frac{8}{3} \]

4. **Calculate the y-coordinate of the Centroid:**
\[ G_y = \frac{y_1 + y_2 + y_3}{3} = \frac{3 + 7 + 1}{3} \]
Simplifying this:
\[ G_y = \frac{11}{3} \]

5. **Combine the Coordinates:**
Therefore, the coordinates of the centroid (point of intersection of the medians) are:
\[ G = \left( \frac{8}{3}, \frac{11}{3} \right) \]

### Final Answer:
The coordinates of the point of intersection of the medians of triangle ABC are \(\left( \frac{8}{3}, \frac{11}{3} \right)\).