Question

X – axis divides the line joining (2, - 5) and (1, 9) in the ratio. ​

Answer 1

Step-by-step explanation:

hope it helps you .please mark me as brainlenst...

Answer 2

Answer:

5 : 9

Step-by-step explanation:

Given,

A = (2 , - 5)

B = (1 , 9)

To Find :-

The ration that which the x-axis divides those co - ordinates.

How To Do :-

As we know that the co - ordinates of x- axis = (x , 0) by using the section(Internal Division ) formula we can find the value of 'm : n'. We need to equate both the 'y' co - ordinates because We are having a constant value in the co-ordinates of 'x' axis so that we can find the ratio.

Formula Required :-

Internal division formula :-

$=\left(\dfrac{mx_2+nx_1}{m+n},,\dfrac{my_2+ny_1}{m+n}\right)$

Solution :-

A = (2 , - 5)

Let,

x₁ = 2 , y₁ = - 5

B = (1 , 9)

Let,

x₂ = 1, y₂ = 9

Let the ration that 'x' axis divides be 'm : n'

$\implies (x,0)=\left(\dfrac{m(1)+(2)n}{m+n},\dfrac{m(9)+n(-5)}{m+n}\right)$

$(x,0)=\left(\dfrac{m+2n}{m+n},\dfrac{9m-5n}{m+n}\right)$

Equating both 'y' co - ordinates :-

$0=\dfrac{9m-5n}{m+n}$

$0\times (m+n)=9m-5n$

0 = 9m - 5n

9m = 5n

9m/n = 5

m/n = 5/9

m : n = 5 : 9

∴ The 'x' - axis divides the co-ordinates in the ration '5 : 9'.