If point `P(3,2)` divides the line segment AB internally in the ratio of `3:2` and point `Q(-2,3)` divides AB externally in the ratio `4:3` then find the coordinates of points A and B.

Answer

`A=((66)/(17),(31)/(17))` and `B=((41)/(17),(36)/(17))`

Explanation

Let `A-=(a,b) and B-=(c,d)`
`P(3,2)` divides AB inernally in the ratio `3:2`.
`therefore(3,2)-=((3c+2a)/(3+2),(3d+2b)/(3+2))`
`therefore 3c+2a=15` (1)
and `3d+2b=10` (2)
`P(-2,3)` divides AB externally in the ratio `4:3`.
`therefore (-2,3)-=((4c-3a)/(4-3),(4d-3b)/(4-3))`
`therefore 4c-3b=3` (3)
and `4d-3b=3` (4)
Solving (1) and (3), we get
`17c=41and 17a=66` ,
Solving (2) and (4), we get
`17d=36and 17b=31`
`therefore A-=((66)/(17),(31)/(17)) and B-=((41)/(17),(36)/(17))`