(Q18) The line joining points A(6,9) and B(-6, -9) is given.

In which ratio does the point Q(-2,-3) divide AB ?

Let Q divide AB in the ratio say k:1 internally, then

Q(-2 , -3) = (
kx2+x1
k+1
 ,
ky2+y1
k+1
 )

[By second formula]

(-2 , -3) = (
k(-6)+
k+1
 ,
k(-9)+
k+1
 )
- 2 =
-6k+
k+1
 and
-9k+
k+1
 = -3

-6k+ = -2k-2 and -9k+ = -3k-3

-6k+2k = -2- and -9k+3k = -3-

-4k = - and -6k = -

k =
-
-4
 = and k =
-
-6
 =

The ratio is k:1 = :1