Question

Find the ratio in which the line segment joining the points A(3,8) and B(–9, 3) is divided by the Y– axis.

Answer 1

Let the ratio in which the line AB is divided by the y-axis be k : 1.
The point on the y - axis be (0, y).
$$\begin{gathered} \left(0,y\right)=\left(\frac{k\times \left(-9\right)+1\times 3}{k+1},\frac{k\times 3+1\times 8}{k+1}\right) \\ \Rightarrow \left(0,y\right)=\left(\frac{-9k+3}{k+1},\frac{3k+8}{k+1}\right) \\ \Rightarrow 0=\frac{-9k+3}{k+1} \\ \Rightarrow -9k+3=0 \\ \Rightarrow k=\frac{1}{3} \end{gathered}$$
Thus, the ratio is 1 : 3.