Question

Find the ratio in which the line segment joining (−2, −3) and (5, 6) is divided by (i) x-axis (ii) y-axis. Also, find the coordinates of the point of division in each case.

Answer 1

The ratio in which the x−axis divides two points and is $\lambda :1$

The ratio in which the y-axis divides two points and is $\mu :1$

The co-ordinates of the point dividing two points and in the ratio is given as,

Where

Here the two given points are A(−2,−3) and B(5,6).

1. The ratio in which the x-axis divides these points is

$$\begin{gathered} \frac{6\lambda -3}{3}=0 \\ \lambda =\frac{1}{2} \end{gathered}$$

Let point P(x, y) divide the line joining ‘AB’ in the ratio

Substituting these values in the earlier mentioned formula we have,

Thus the ratio in which the x−axis divides the two given points and the co-ordinates of the point is.

2. The ratio in which the y-axis divides these points is

$$\begin{gathered} \frac{5\mu -2}{3}=0 \\ \Rightarrow \mu =\frac{2}{5} \end{gathered}$$

Let point P(x, y) divide the line joining ‘AB’ in the ratio

Substituting these values in the earlier mentioned formula we have,

Thus the ratio in which the x-axis divides the two given points and the co-ordinates of the point is.