Find the coordinates of the point P which divides the line joining of A(-2,5) and B (3,-5) in the ratio 2 : 3 .

Answer

To find the coordinates of the point P that divides the line segment joining points A(-2, 5) and B(3, -5) in the ratio 2:3, we can use the section formula.

### Step-by-Step Solution:

1. **Identify the coordinates of points A and B**:
- A = (-2, 5) → (x1, y1)
- B = (3, -5) → (x2, y2)

2. **Identify the ratio in which point P divides the line segment**:
- The ratio is given as 2:3, where m = 2 and n = 3.

3. **Apply the section formula**:
The section formula states that if a point P divides the line segment joining points A(x1, y1) and B(x2, y2) in the ratio m:n, then the coordinates (x, y) of point P can be calculated as follows:
\[ x = \frac{mx_2 + nx_1}{m+n} \]
\[ y = \frac{my_2 + ny_1}{m+n} \]

4. **Substitute the values into the formula**:
- For x-coordinate:
\[ x = \frac{2 \cdot 3 + 3 \cdot (-2)}{2 + 3} = \frac{6 - 6}{5} = \frac{0}{5} = 0 \]

- For y-coordinate:
\[ y = \frac{2 \cdot (-5) + 3 \cdot 5}{2 + 3} = \frac{-10 + 15}{5} = \frac{5}{5} = 1 \]

5. **Combine the coordinates to find point P**:
- Therefore, the coordinates of point P are (0, 1).

### Final Answer:
The coordinates of point P are (0, 1).