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

Let the ratio k : 1

= Using section formula,

$x=\frac{5 \times k+1 \times-1}{k+1}$

$\Rightarrow x=\frac{5 k-1}{k+1}$

$y=\frac{7 \times k+1 \times 1}{k+1}$

$y=\frac{7 k+1}{k+1}$

Putting the value of x and y in the equation of line, we get

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

$12 k=4(k+1)$

$\Rightarrow 12 k=4 k+4$

$8 k=4$

$k=\frac{1}{2}$

$\therefore$ Ratio is $1: 2 .$