Question

Find the ratio in which the y-axis divides the segment joining $(-3,6)$ and $(12,-3)$.

Answer 1

Equation of line joining $(-3,6)$ and $(12,-3)$

$y-y_1=\left(\frac{y_2-y_1}{x_2-x_1}\right)(x-x_1)$

$⟹y-6=\left(\frac{-3-6}{12+3}\right)(x+3)$

$⟹3x+5y=21$

When it crosses $y-$axis $x=0$

$⟹3\times 0+5y=21$

$⟹y=\frac{21}{5}$

Let ratio be $\lambda :1$

$\frac{m{x}_2+n{x}_1}{m+n}=0⟹\frac{12\lambda -3}{\lambda +1}$

$⟹\lambda =\frac{1}{4}$

Ratio is $1:4$