search
Log In
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
0 votes
97 views

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 9.2k points 31 508 811
recategorized by
97 views

1 Answer

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)

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

238 points 2 2 4

Related questions

0 votes
0 answers
1
79 views
Let $(x_{1},4),(-2,y_{1})$ lies on the line joining the points $(2,-1),(5,-3)$ then the point $P(x_{1},y_{1})$ lies on the line: $6(x+y)-25=0$ $2x+6y+1=0$ $2x+3y-6=0$ $6(x+y)+25=0$
asked Apr 1, 2020 in Quantitative Aptitude Lakshman Patel RJIT 9.2k points 31 508 811 79 views
0 votes
0 answers
2
57 views
The image of the point $\left (3, 8 \right)$ in the line $x+3y=7$ is : $\left (1, 4 \right)$ $\left (4, 1 \right)$ $\left (-1, -4 \right)$ $\left (-4, -1 \right)$
asked Apr 3, 2020 in Quantitative Aptitude Lakshman Patel RJIT 9.2k points 31 508 811 57 views
0 votes
1 answer
3
115 views
The minute hand is $10$ cm long. Find the area of the face of the clock described by the minute hand between $9$ a.m and $9:35$ a.m. ${183.3\ cm^{2}}$ ${366.6\ cm^{2}}$ ${244.4\ cm^{2}}$ ${188.39\ cm^{2}}$
asked Apr 1, 2020 in Quantitative Aptitude Lakshman Patel RJIT 9.2k points 31 508 811 115 views
0 votes
0 answers
4
61 views
Determine $a+b$ such that the following system of equations: $2x-(a-4)y=2b+1 \text{ and }4x-(a-1)y=5b-1$ infinite solutions. $11$ $9$ $10$ $8$
asked Apr 1, 2020 in Quantitative Aptitude Lakshman Patel RJIT 9.2k points 31 508 811 61 views
0 votes
0 answers
5
93 views
Which of the following statement is false? ... Statement(iii) Statement(ii) Statement(iv) Statement(i)
asked Apr 1, 2020 in Quantitative Aptitude Lakshman Patel RJIT 9.2k points 31 508 811 93 views
...