The coordinates of a point which divides the join of (5, -5) and (2, - 3) in the ratio 4 : 3, externally, are:

Options

A. (3, 4)
B. (-7, 3)
C. (- 7, 9)
D. (8, 3)

Answer

To find the coordinates of the point that divides the line segment joining the points (5, -5) and (2, -3) in the ratio 4:3 externally, we will use the formula for external division.

### Step-by-Step Solution:

1. **Identify the Points and the Ratio**:
- Let point A = (5, -5) and point B = (2, -3).
- The ratio in which the point P divides the line segment externally is given as 4:3.

2. **Assign Values**:
- Let m = 4 (the part of the ratio associated with point B)
- Let n = 3 (the part of the ratio associated with point A)

3. **Use the External Division Formula**:
The coordinates (x, y) of the point P that divides the segment externally in the ratio m:n is given by:
\[ x = \frac{m \cdot x_2 - n \cdot x_1}{m - n} \]
\[ y = \frac{m \cdot y_2 - n \cdot y_1}{m - n} \]
where (x1, y1) are the coordinates of point A and (x2, y2) are the coordinates of point B.

4. **Substitute the Values**:
- For x-coordinate:
\[ x = \frac{4 \cdot 2 - 3 \cdot 5}{4 - 3} = \frac{8 - 15}{1} = \frac{-7}{1} = -7 \]
- For y-coordinate:
\[ y = \frac{4 \cdot (-3) - 3 \cdot (-5)}{4 - 3} = \frac{-12 + 15}{1} = \frac{3}{1} = 3 \]

5. **Final Coordinates**:
Thus, the coordinates of point P that divides the line externally in the ratio 4:3 are:
\[ P = (-7, 3) \]

### Conclusion:
The coordinates of the point which divides the join of (5, -5) and (2, -3) in the ratio 4:3 externally are (-7, 3).