Question

(i) In what ratio is the line segment joining the points (-2, -3) and (3, 7) divided by the y-axis ? Also, find the coordinates of the point of division.

(ii) In what ratio is the line segment joining (-3, -1) and (-8, -9) divided at the point $(-5,\frac{-21}{5})?$

Answer 1

i) Let the ratio in which the line is divided be a:1 and the point of division be (0,y)
So, $0=\frac{3a-2}{a+1}$

$\Rightarrow a=\frac{2}{3}$

Now, $y=\frac{7\times \frac{2}{3}-3}{\frac{2}{3}+1}=1$

So, the point is (0,1).

ii) Let the ratio in which the line is divided be k:1.

So, $-5=\frac{-8k-3}{k+1}$

$\Rightarrow -5k-5=-8k-3$

$\therefore k=\frac{2}{3}$