Question

If CR : RS = 2:3 and RS: SD = 5:6, then S divides line segment CD in the ratio​

Answer 1

Answer:

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's assume the joining points as A (2,−3) and B (5,6) be divided by point P (x,0) in the ratio k:1.

Then , we have,

y=

k+1

ky

2

+y

1

0=

k+1

6k+(−3)

0=6k−3

k=

2

1

Hence , the required ratio is 1:2.

Answer 2

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

the line joining the points (x1 ,y 1 ) and (x 2 ,y 2 ) in the ratio m:n, then

(x,y)=( m+n mx 2 +nx 1 , m+n m y 2 +ny 1 )

Substituting (x 1 ,y 1 )=(2,−3) and (x 2 ,y 2 )=(5,6) in the section formula,

we get the point ( m+n m(5)+n(2) , m+n m(6)+n(−3) )

Since the point of intersection lies on the x - axis, y - coordinate =0

m+n

6m−3n

=0

=>6m−3n=0

=>6m=3n

2m=n

=>m:n=1:2