Question

Find the ratio in which the y-axis divides the line segment joining the points (-4,-6) and (10,12). Also find the coordinates of the point of division.

Answer 1

Let the y-axis divide the line segment joining the points (-4, -6) and (10, 12) in the ratio $\lambda :1$ and the Point of the intersection be (0, y).
So, by section formula, we have :
$(\frac{10\lambda +(-4)}{\lambda +1},\frac{12\lambda +(-6)}{\lambda +1})=(0,y)\therefore \frac{10\lambda -4}{\lambda +1}=0\Rightarrow 10\lambda -4=0\Rightarrow \lambda =\frac{4}{10}=\frac{2}{5}$
Therefore, $y=\frac{12\lambda +(-6)}{\lambda +1}=\frac{12\times \frac{2}{5}-6}{\frac{2}{5}+1}=\frac{\left(\frac{24-30}{5}\right)}{\left(\frac{2+5}{5}\right)}=-\frac{6}{7}$
Thus, they - axis divides the line segment joining the given points in the ratio 2 : 5 and the point of division is $(0,-\frac{6}{7})$.