Find the co-ordinates of a point which divides the line segment joining the points (1, -3) and (2, -2) in the ratio 3 : 2 externally.

Answer

To find the coordinates of a point that divides the line segment joining the points (1, -3) and (2, -2) in the ratio 3:2 externally, we can use the external section formula.

### Step-by-Step Solution:

1. **Identify the Points and the Ratio**:
- Let the points be \( A(1, -3) \) and \( B(2, -2) \).
- The ratio in which the point divides the line segment is \( m:n = 3:2 \).

2. **Use the External Section Formula**:
The external section formula for a point \( P(x, y) \) that divides the line segment joining points \( A(x_1, y_1) \) and \( B(x_2, y_2) \) in the ratio \( m:n \) is given by:
\[ x = \frac{m \cdot x_2 - n \cdot x_1}{m - n} \]
\[ y = \frac{m \cdot y_2 - n \cdot y_1}{m - n} \]

3. **Substituting the Values**:
- Here, \( x_1 = 1 \), \( y_1 = -3 \), \( x_2 = 2 \), \( y_2 = -2 \), \( m = 3 \), and \( n = 2 \).
- For \( x \):
\[ x = \frac{3 \cdot 2 - 2 \cdot 1}{3 - 2} = \frac{6 - 2}{1} = \frac{4}{1} = 4 \]
- For \( y \):
\[ y = \frac{3 \cdot (-2) - 2 \cdot (-3)}{3 - 2} = \frac{-6 + 6}{1} = \frac{0}{1} = 0 \]

4. **Final Coordinates**:
- Therefore, the coordinates of the point that divides the line segment externally in the ratio 3:2 are \( (4, 0) \).

### Final Answer:
The coordinates of the required point are \( (4, 0) \).