Question

Find the ratio in which the $y-$axis divides the line segment joining the points $(5,-6)$ and $(-1,-4)$. Also find the point of intersection.

Answer 1

Let the point be $A(5,-6)$, $B(-1,-4)$ and $P(0,y)$

Point $P$ is on $y-$axis,hence its $x$ co-ordinate is $0$.So, it is of the form $P(0,y)$

Now, we have to find ratio.

Let the ratio be $k:1$

Hence $m_1=k$, $m_2=1$, $x_1=5$, $y_1=-6$, $x_2=-1$,$y_2=-4$, $x=0$, $y=0$

Using sections formula $x=\frac{m_1{x}_2+m_2{x}_1}{m_1+m_2}$

$\Rightarrow 0=\frac{-k+5}{k+1}$

$\therefore k=5$

Again $y=\frac{m_1{y}_2+m_2{y}_1}{m_1+m_2}$

$=\frac{-4k-6}{k+1}=\frac{-20-6}{6}$ for $k=5$

$=\frac{-13}{3}$

Hence the coordiantes of point is $P(0,\frac{-13}{3})$