Lakshman Patel RJIT
asked
in Quantitative Aptitude
Apr 1, 2020
recategorized
Nov 8, 2020
by Krithiga2101

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Ans is option (C)

By using the two point form of equation of a straight line, (for the points $(-1,1)$ and $(5,7)$)

$y-y_{1}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\times(x-x_{1})$

By substituting the points in the given formula, we get the equation of the straight line as $y=x+2$

So, now the intersection point of $y=x+2$ and $x+y=4$ is $(1,3)$

Since the line $x+y=4$ divides the line $y=x+2$ in the ratio $\lambda:1$, we use the section formula to determine the value of $\lambda.$ (Ref: Section Formula)

$\therefore$ $\frac{\lambda(5)+1(-1)}{\lambda+1}=1$ $\Rightarrow$ $4\lambda=2$ $\Rightarrow$ $\lambda=\frac{1}{2}$

0 votes

Answer is C

Another method of solving the above problem.

Ratio is $\lambda :1$ and points given are (-1, 1) and (5, 7)

Therefore, point is $(\frac{5\lambda -1}{\lambda +1}, \frac{7\lambda +1}{\lambda +1})$

This point lies on the given line x + y = 4

$\frac{5\lambda -1}{\lambda +1} + \frac{7\lambda +1}{\lambda +1} =4$

On solving, we get value of ${\lambda} = \frac{1}{2}$

Another method of solving the above problem.

Ratio is $\lambda :1$ and points given are (-1, 1) and (5, 7)

Therefore, point is $(\frac{5\lambda -1}{\lambda +1}, \frac{7\lambda +1}{\lambda +1})$

This point lies on the given line x + y = 4

$\frac{5\lambda -1}{\lambda +1} + \frac{7\lambda +1}{\lambda +1} =4$

On solving, we get value of ${\lambda} = \frac{1}{2}$