(i) At what ratio is the segment joining the points $(-2,-3)$ and $(3,7)$ divides by the y-axis? find out the coordinates of the point of division.(ii) At what ratio is the line segment joining $(-3,-1)$ and $(-8,-9)$ divided at the point $(-5, -21/5)$?

Let’s consider P$(-2,-3)$ and Q$(9,3)$ be the given points.

Let’s Suppose we have the y-axis that divides PQ in the ratio k:$1$ at R($0$, y)

So, the coordinates of R are as given below

Now, on equating we get

$3k–2=0$

$k=2/3$

So, the ratio is $2:3$

Putting k$=2/3$ in the coordinates of R, we get

R $(0,1)$

Let’s take into account   A$(-3,-1)$ and B$(-8,-9)$ be the given points.

And, let’s consider P be the point that divides AB in the ratio k:$1$

Therefore, the coordinates of P are given

But ,we have given the coordinates of P

On equating, we get

$(-8k–3)/(k +1)=-5$

$-8k–3=-5k–5$

$3k=2$

K$=2/3$

Therefore, the point P divides AB in the ratio $2:3$