In each of the following examples find the co-ordinates of point A with divides segment `PQ` in the ratio `a : b`.
`P(-2,-5), Q(4,3), a : b = 3 : 4`

Explanation

`P(-2,-5)` and `Q(4,3)`.
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)=-2,y_(1)=-5,x_(2)=4` and `y_(2)=3`.
A divides PQ in the ratio`a:b`.
`a:b=3:4`
By section formula
`x=(ax_(2)+bx_(1))/(a+b), y=(ay_(2)+by_(1))/(a+b)`
`:.x=(3(4)+4(-2))/(3+4),:.y=(3(3)+4(-5))/(3+4)`
`:.x=(12-8)/7, :.y=(9-20)/7`
`:.x=4/7,:y.y=(-11)/7`
The coordinates of point A are `(4/7,(-11)/7)`.