Question

In what ratio does the point $(-4,6)$ divide the line segment joining the points $A(-6,10)$ and $B(3,-8)$?

Answer 1

Point dividing a line in the ratio $1:m$ formed by joining $(x_1,y_1)$ and $(x_2,y_2)$ is given by

$x=\frac{m{x}_1+x_2}{1+m}$ $y=\frac{m{y}_1+y_2}{1+m}$

We have the points $A(-6,10)$ and $B(3,-8).$
Let the point $(-4,6)$ divide the line joining $AB$ in the ratio $1:m.$

$-4=\frac{-6m+3}{1+m}$

$-4-4m=-6m+3$

$2m=7$

$m=\frac{7}{2}$

$1:m=1:\frac{7}{2}=1\times 2:\frac{7}{2}\times 2=2:7$
So the point divides the line in the ratio $2:7.$