In each of the following examples find the co-ordinates of point A with divides segment `PQ` in the ratio `a : b`.
`P (2, 6), Q(-4, 1) , a: b = 1: 2`

Explanation

`P(2,6)` and `Q(-4,1)`.
Let coordinates of point A be `(x,y)`.
Suppose coordinates of point P are e`(x_(1),y_(1))` and Q are `(x_(2),y_(2))` then `x_(1)=2,y_(1)=6,x_(2)=-4` and `y_(2)=1`
A divides PQ in the ratio `a:b`.
`a:b=1:2`
By section formula,
`x=(ax_(2)+bx_(1))/(a+b), y=(ay_(2)+by_(1))/(a+b)`
`:.x=(1(-4)+2(2))/(1+2),:.y=(1(1)+2(6))/(1+2)`
`:.x=(-4+4)/3,:.y=(1+12)/3`
`:.x=0/3, :.y=13/3`
`:.x=0`
The coordinates of point A are `(0,13/3)`.