In each of the following examples find the co-ordinates of point A with divides segment `PQ` in the ratio `a : b`.
`P(-3,7),Q(1,-4),a : b = 2:1`

Explanation

`P(-3,7)` and `Q(1,-4)`
Let coordinates of point A be `(x,y)`.
Suppose coordinates of point P are `(x_(1),y_(1))` and Q are `(x_(2),y_(2))`
then `x_(1)=-3,y_(1)=7,x_(2)=1` and `y_(2)=-4`
A divided PQ in the ratio `a:b`.
` a:b=2:1`
By section formula,
`x=(ax_(2)+bx_(1))/(a+b),y=(ay_(2)+by_(1))/(a+b)`
`:.x=(2(1)+1(-3))/(2+1) , :. y=(2(-4)+1(7))/(2+1)`
`:.x=(2-3)/3, :.y=(-8+7)/3`
`:x=-1/3, ,.y=(-1)/3`
The coordinates of point A are `((-1)/3,(-1)/3)`.