The points A `(x_(1),y_(1)), B (x_(2),y_(2)) and C (x_(3),y_(3))` are the vertices of `Delta ABC`.
What are coordinate of the centroid of the triangle ABC ?

Answer

To find the coordinates of the centroid of triangle ABC with vertices A \((x_1, y_1)\), B \((x_2, y_2)\), and C \((x_3, y_3)\), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Definition of Centroid**:
The centroid of a triangle is the point where the three medians intersect. It can also be thought of as the average of the vertices' coordinates.

2. **Formula for the Centroid**:
The coordinates of the centroid (G) can be calculated using the formula:
\[ G\left(x_G, y_G\right) = \left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) \]

3. **Calculate the x-coordinate of the Centroid**:
Using the formula:
\[ x_G = \frac{x_1 + x_2 + x_3}{3} \]

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

5. **Combine the Results**:
Therefore, the coordinates of the centroid G are:
\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) \]

### Final Answer:
The coordinates of the centroid of triangle ABC are:
\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) \]