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, −21/5)?

Answer 1

(i) The ratio in which the y-axis divides two points and is $\lambda :1$

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(3,7).

Since, the point is on the y-axis so, x coordinate is 0.
$$\begin{gathered} \frac{3\lambda -2}{1}=0 \\ \Rightarrow \lambda =\frac{2}{3} \end{gathered}$$

Thus the given points are divided by the y-axis in the ratio.

The co-ordinates of this point (x, y) can be found by using the earlier mentioned formula.

Thus the co-ordinates of the point which divides the given points in the required ratio are.

(ii) The co-ordinates of a point which divided two points and internally in the ratio is given by the formula,

Here it is said that the point divides the points (−3,−1) and (−8,−9). Substituting these values in the above formula we have,

Equating the individual components we have,

Therefore the ratio in which the line is divided is.