(Q20) Find the ratio in which the y-axis divides the line segment joining the points (5,-6) and(-1,-4).Also find the point of intersection .

Answer

Let the ratio be K:1. Then by the section formula, the coordinates of the point which divides AB in the ratio K:1 are

(
K(-1)+1()
K+1
 ,
K(-4)+1(-)
K+1
)
= (
-k+
K+1
 ,
-4k-
K+1
)

the point lies on the y-axis and we know that on the Y-axis the abscissa is 0

Therefore
-k+
K+1
 =0

-k+=0

K=

So the ratio is K:1 = :1

Putting the value of K= we get the point of intersection as

= (
-+
5+1
 ,
-4()-
5+1
)
= (,
-
6
) = (,
-
3
)