Find the co-ordinates of the point which divides the join of the point (2,3) and (6,8) externally in the ratio 4:3.

Options

A. a. (15,16)
B. b. (18,23)
C. c. (3,8)
D. d. (2,7)

Answer

To find the coordinates of the point that divides the line segment joining the points (2, 3) and (6, 8) externally in the ratio 4:3, we can use the formula for external division.

### Step-by-Step Solution:

1. **Identify the Points and Ratio**:
- Let the points be \( A(2, 3) \) and \( B(6, 8) \).
- The ratio in which the point divides the segment externally is \( m:n = 4:3 \).

2. **Use the External Division Formula**:
- The formula for the coordinates \( (x, y) \) of the point that divides the line segment externally in the ratio \( m:n \) is given by:
\[ x = \frac{m \cdot x_2 - n \cdot x_1}{m - n} \]
\[ y = \frac{m \cdot y_2 - n \cdot y_1}{m - n} \]
- Here, \( (x_1, y_1) = (2, 3) \) and \( (x_2, y_2) = (6, 8) \).

3. **Substituting the Values for x-coordinate**:
- Substitute \( m = 4 \), \( n = 3 \), \( x_1 = 2 \), and \( x_2 = 6 \):
\[ x = \frac{4 \cdot 6 - 3 \cdot 2}{4 - 3} \]
\[ x = \frac{24 - 6}{1} = \frac{18}{1} = 18 \]

4. **Substituting the Values for y-coordinate**:
- Now substitute for the y-coordinate:
\[ y = \frac{4 \cdot 8 - 3 \cdot 3}{4 - 3} \]
\[ y = \frac{32 - 9}{1} = \frac{23}{1} = 23 \]

5. **Final Coordinates**:
- Therefore, the coordinates of the point that divides the line segment externally in the ratio 4:3 are \( (18, 23) \).

### Final Answer:
The coordinates of the point are \( (18, 23) \).