(Q16) The line joining points A(6,9) and B(-6, -9) is given.In which ratio does the origin divide AB and what is it called for AB ?

Given A(6,9) , B(-6,-9)

Let origin O (0,0) divides AB in the ratio k:1 internally

[By section formula] O(0,0) = (
kx2+x1
k+1
 ,
ky2+y1
k+1
 )
(0,0) = (
k(-)+
k+1
 ,
k(-)+
k+1
 )
0 =
-k+
k+1

-k+ = 0

k =

k =

0 =
-k+
k+1

-k+ = 0

k =

k =

The ratio is :

Here the origin bisects AB.

∴ Origin is called the midpoint of AB.