Question

The ratio in which the line $x+y=4$ divides the line joining the points $(-1,1)$ and $(5,7)$ is

• A. $1:2$
• B. $2:1$
• C. $3:2$
• D. $3:1$

Answer 1

The correct option is A $1:2$

Solution:

The given points are $(-1,1)$ and $(5,7)$.

Hence equation of the line joining the above points is

$\frac{y-1}{7-1}=\frac{x-(-1)}{5-(-1)}$

$\frac{y-1}{6}=\frac{x+1}{6}$

$y-1=x+1$

$x-y+2=0---------\left(1\right)$

Equation of the given line is

$x+y-4=0---------\left(2\right)$

The point of intersection of the lines (1) and (2) is

$x-y=-2$

$x+y=4$

$2x=2$

$x=1,y=3$

Let the point $(1,3)$ divide the line segment joining $(-1,1)$ and $(5,7)$ in the ratio $1:k$

By applying the section formula,

$1=\frac{k(-1)+1\left(5\right)}{k+1}$

$\Rightarrow k+1=-k+5$

$\Rightarrow 2k=4$

$k=2$

Hence the line joining the points$(-1,1)$and $(5,7)$is divided by line

$x+y=4$ in the ratio $1:2$