Question

In what ratio, the line joining (-1,1) and (5,7) is divided by the line x+y=4?

Answer 1

The equation of given line is
$x+y-4=0$
Let the given line divide the line joining A(-1,1) and B(5,7) in the ratio k:1 at point
Then coordinates of C are
$[\frac{5k-1}{k+1},\frac{7k+1}{k+1}]$

Since the point lies on the given line

$\therefore \frac{5k-1}{k+1}+\frac{7k+1}{k+1}-4=0$

$\Rightarrow 5k-1+7k+1-4k-4=0$

$\Rightarrow 8k=4\Rightarrow k=\frac{1}{2}$

The required is $\frac{1}{2}$: 1 i.e. 1:2.