Question

Find the radio does the x axis divides the line segment joining A(2,-3)B(5,6)

Answer 1

Answer:

Step-by-step explanation:

Using the section formula, if a point (x,y) divides the line joining the points (x  

1

​  

,y  

1

​  

) and (x  

2

​  

,y  

2

​  

) in the ratio m:n, then  

(x,y)=(  

m+n

mx  

2

​  

+nx  

1

​  

 

​  

,  

m+n

my  

2

​  

+ny  

1

​  

 

​  

)

Let the required ratio be λ:1 then, the coordinates of the point of division are,

R(  

λ+1

5λ+2

​  

,  

λ+1

6λ−3

​  

)

But, it is a point on x-axis on which y-coordinates of every point is zero.

∴  

λ+1

6λ−3

​  

=0⇒λ=  

2

1

​  

 

Thus,the required ratio is  

2

1

​  

:1 or 1:2.

Putting λ=  

2

1

​  

 in the coordinates of R, we find that its coordinates are (3,0)