Question

find the ratio in which the line joining the points (6 3) and (3 -5) is divided by the x-axis

Answer 1

hope this will help u

Answer 2

Answer:

The ratio in which the line joining the given points is dividef by the x - axis is 3 : 5

Step-by-step explanation:

Given,

Two points are ( 6 , 3 ) and ( 3 , - 5) ,therefore,

x₁ = 6 , y₁ = 3

x₂ = 3 , y₂ = -5

Let us suppose the ratio be m₁ : m₂

Let P ( x , y ) be the point of intersection of the line segment and the x- axis

By the section formula we know,

x =  $\frac{m_{1}x_{2}+m_{2}x_{1}}{m_{1}+m_{2}}$

y =  $\frac{m_{1}y_{2}+m_{2}y_{1}}{m_{1}+m_{2}}$

Substituting the values of x₁ , x₂ , y₁ , y₂

x = $\frac{3m_{1}+6m_{2}}{m_{1}+m_{2}}$

y =  $\frac{-5m_{1}+3m_{2}}{m_{1}+m_{2}}$

The equation of x- axis is y = 0

⇒ y =  $\frac{-5m_{1}+3m_{2}}{m_{1}+m_{2}}$ = 0

-5m₁ + 3m₂ = 0

-5m₁ = -3m₂

5m₁ = 3m₂

⇒ $\frac{m_{1}}{m_{2}} = \frac{3}{5}$

m₁ : m₂ = 3 : 5

Hence,

The ratio in which the line joining the given points is divided by the x - axis is 3 : 5