Question

In what ratio the line $x+y=4$ divides the line joining the points $(-1,1)$ and $(5,7)?$

Answer 1

The ratio that the line $ax+by+c=0$ divides the line joining the points $(x_1,y_1),(x_2,y_2)$ is

$-(a{x}_1+b{y}_1+c):(a{x}_2+b{y}_2+c)$

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

$=-(-1+1-4):(5+7-4)$

$=-(-4):8$

$=4:8$

$=1:2$(Ans)