in Quantitative Aptitude recategorized by
375 views
0 votes
0 votes

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
12.0k points
375 views

1 Answer

0 votes
0 votes

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)

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

438 points

Related questions

Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true