# In what ratio is the line segment joining the points A

Question:

In what ratio is the line segment joining the points A(-4, 2) and B(8, 3) divided by the y-axis? Also, find the point of intersection.

Solution:

Let the point which cuts the join of A(-4, 2) and B(8, 3) in the ratio k : 1 be P(0, y)

Formula: If $\mathrm{k}: 1$ is the ratio in which the join of two points are divided by another point $(x, y)$, then

$\mathrm{x}=\frac{\mathrm{kx}_{2}+\mathrm{x}_{1}}{\mathrm{k}+1}$

$\mathrm{y}=\frac{\mathrm{ky}_{2}+\mathrm{y}_{1}}{\mathrm{k}+1}$

Taking for the x co-ordinate,

$0=\frac{\mathrm{k} \times 8+(-4)}{\mathrm{k}+1}$

$\Rightarrow 8 \mathrm{k}=4$

$\Rightarrow \mathrm{k}=\frac{1}{2}$

Therefore,

$y=\frac{\frac{1}{2} \times 3+2}{\frac{1}{2}+1}$

$y=\frac{3+4}{1+2}$

$y=\frac{7}{3}$

Therefore, the ratio in which the line segment joining the points A(-4, 2) and B(8, 3)

divided by the y-axis is 1 : 2 and the point of intersection is $\left(0, \frac{7}{3}\right)$