Find the ordinate of the point at which the straight line joining the point (2,-3) , (-3,7) is divided externally in the ratio 5 : 3

Options

A. 22
B. 20
C. 18
D. 13

Answer

To find the ordinate (y-coordinate) of the point at which the straight line joining the points (2, -3) and (-3, 7) is divided externally in the ratio 5:3, we can use the formula for external division.

### Step-by-Step Solution:

1. **Identify the Points and Ratios**:
- Let the points be \( A(2, -3) \) and \( B(-3, 7) \).
- The ratio of division is \( m_1:m_2 = 5:3 \).

2. **Assign Values**:
- From the points, we have:
- \( x_1 = 2, y_1 = -3 \)
- \( x_2 = -3, y_2 = 7 \)
- The values for the ratio are:
- \( m_1 = 5, m_2 = 3 \)

3. **Use the Formula for External Division**:
- The formula for the y-coordinate \( y \) when dividing externally is given by:
\[ y = \frac{m_1 y_2 - m_2 y_1}{m_1 - m_2} \]

4. **Substitute the Values into the Formula**:
- Substitute \( m_1, m_2, y_1, y_2 \) into the formula:
\[ y = \frac{5 \cdot 7 - 3 \cdot (-3)}{5 - 3} \]

5. **Calculate the Numerator**:
- Calculate \( 5 \cdot 7 = 35 \)
- Calculate \( 3 \cdot (-3) = -9 \) (note that this becomes positive when subtracted)
- Thus, the numerator becomes:
\[ 35 + 9 = 44 \]

6. **Calculate the Denominator**:
- The denominator is:
\[ 5 - 3 = 2 \]

7. **Final Calculation**:
- Now, substitute the values back into the equation:
\[ y = \frac{44}{2} = 22 \]

8. **Conclusion**:
- The ordinate of the point is \( 22 \).

### Final Answer:
The ordinate of the point is \( 22 \).