Question

find the ratio in which the line joining points (-4,7) and (3,0) is divided by y-axis​

Answer 1

Given

Two points A(-4,7) B(3,0)

To Find

Ratio in which line divides the points

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

Let us assume that M (0,y) be a point on y axis

which divides the line segment PQ in the ratio k:1.

[Note:On y axis x is zero and on x axis y is zero.]

By using section formula

Finding x coordinate :

$\sf \longmapsto0 = \dfrac{m_{1}x_{2} + m_{2}x_{1}}{m + n}$

$\sf \longmapsto 0 = \dfrac{k \times 3 + 1 \times ( - 4)}{k + 1}$

$\sf \longmapsto0 = \dfrac{3k - 4}{k + 1}$

$\sf \longmapsto3k = 4$

$\sf \longmapsto \: k = \dfrac{4}{3}$

Now , finding y coordinate

$\sf \longmapsto \: y = \dfrac{m_{1}y_{2}+ m_{2}y_{1}}{m + n}$

$\sf \longmapsto \: y = \dfrac{m \times 0 + 1 \times 7}{k + 1}$

$\sf \longmapsto \: y = \dfrac{7}{k + 1}$

$\sf \longmapsto \: y = \dfrac{7}{ \dfrac{4}{3} + 1} = \dfrac{7}{ \dfrac{7}{3} } = 3$

$\sf \bold{y = 3}$

∴ The required ratio is 4:3 and required point is M (0,3)