Question

In what ratio does the y-axis divide the line segment joining the point P(-4,5) and Q(3,-7)? Also, find the coordinates of the point of intersection.

Answer 1

Using the section formula, if a point $(x,y)$ divides the line joining the points $(x_1,y_1)$ and $(x_2,y_2)$ in the ratio $m:n$, then

$(x,y)=(\frac{m{x}_2+n{x}_1}{m+n},\frac{m{y}_2+n{y}_1}{m+n})$

Suppose y-axis divides PQ in the ratio $K:1$. Then the co-ordinates of the point of division are
$R(\frac{3K-4}{K+1},\frac{-7K+5}{K+1})$
Since, R lies on y-axis and X Co-ordinate of every point on y-axis is zero.
$\therefore \frac{3K-4}{K+1}=0$
$\Rightarrow 3K-4=0\Rightarrow K=\frac{4}{3}$
Hence, the required ratio is $4/3:1$ i.e., $4:3$
Putting $K=4/3$ in the Co-ordinate of R, we find that its Co-ordinate are $(0,-13/7)$