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The line $x+y=4$ divides the line joining $\text{(-1,1)  & (5,7)}$ in the ratio $\lambda : 1$ then the value of $\lambda$ is:

  1. $2$
  2. $3$
  3. $\dfrac{1}{2}$
  4. $1$
in Quantitative Aptitude recategorized by
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1 Answer

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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 $(5,7)$)


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)

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

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