Find the co-orduinates of the point which divides the join of the points (2, 4) and (6, 8) externally in the ratio `5 : 3` :

Options

A. (5, 6)
B. (12, 14)
C. (3, 8)
D. (2, 7)

Answer

To find the coordinates of the point that divides the line segment joining the points \( A(2, 4) \) and \( B(6, 8) \) externally in the ratio \( 5:3 \), we will use the section formula for external division.

### Step-by-Step Solution:

1. **Identify the Points and the Ratio**:
- Let \( A(2, 4) \) and \( B(6, 8) \).
- The ratio in which the point divides the line segment is \( L:M = 5:3 \).

2. **Use the Section Formula for External Division**:
- The section formula for external division is given by:
\[ \left( \frac{Lx_2 - Mx_1}{L - M}, \frac{Ly_2 - My_1}{L - M} \right) \]
- Here, \( L = 5 \), \( M = 3 \), \( (x_1, y_1) = (2, 4) \), and \( (x_2, y_2) = (6, 8) \).

3. **Calculate the x-coordinate**:
- Substitute the values into the formula:
\[ x = \frac{5 \cdot 6 - 3 \cdot 2}{5 - 3} \]
- Calculate:
\[ x = \frac{30 - 6}{2} = \frac{24}{2} = 12 \]

4. **Calculate the y-coordinate**:
- Substitute the values into the formula:
\[ y = \frac{5 \cdot 8 - 3 \cdot 4}{5 - 3} \]
- Calculate:
\[ y = \frac{40 - 12}{2} = \frac{28}{2} = 14 \]

5. **Final Coordinates**:
- The coordinates of the point that divides the line segment externally in the ratio \( 5:3 \) are \( (12, 14) \).

### Conclusion:
Thus, the required coordinates are \( (12, 14) \).

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