Calculate the ratio in which the line joining points A(-1,2) and B(5,7) is divided by the line x=2.

4 : 5

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3 :2

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1 : 1

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9 : 4

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Solution

The correct option is C
1 : 1

Let the point (2,y) divide the line joining the points A(-1,2)and B(5,7) in the ratio $m_{1} : m_{2}$

$∴ x = \frac{m_{1} x_{2} + m_{2} x_{1}}{m_{1} + m_{2}}$

$\begin{matrix} A (- 1, 2) \Rightarrow x_{1} = - 1 y_{1} = 2 B (5, 7) \Rightarrow x_{2} = 5 y_{2} = 7 \end{matrix}$

$2 = \frac{m_{1} x_{2} + m_{2} x_{1}}{m_{1} + m_{2}}$

$2 = \frac{m_{1} (5) + m - 2 (- 1)}{m_{1} + m_{2}}$

$2 m_{1} + 2 m_{2} = 5 m_{1} - m_{2}$

$\begin{matrix} 3 m_{2} = 3 m_{1} \frac{m_{1}}{m_{2}} = \frac{1}{1} \end{matrix}$

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