Question

Find the ratio in which the line segment joining the points A (3, 8) and B1-9, 3) is divided by the Y-axis. ​

Answer 1

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 ratio in which the line AB is divided by the y−axis be k:1.

The point on the y− axis be (0,y).

(0,y)=(

k+1

k×(−9)+1×3

​

,

k+1

k×3+1×8

​

)

⇒(0,y)=(

k+1

−9k+3

​

,

k+1

3k+8

​

)

⇒0=

k+1

−9k+3

​

⇒−9k+3=0

⇒k=

3

1

​

Thus, the ratio is 1:3.