(Q17) The line joining points A(6,9) and B(-6, -9) is given.

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

Given A(6,9) , B(-6,-9) and P(2,3) divide AB internally in the ratio say k:1

[By section formula]

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

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

8k = -2 and 3k+9k = -3

k =
8
 and 12k =
k =
2
 and k =
12
k =
2
The ratio (k:1) = (
2
 :1) = :1