Find the co-ordinates of point P if P divides the line segment joining the points `A(-1,7) and B(4,-3)` in the ratio `2:3`

Explanation

`A(-1,7)` and `B(4,-3)`.
Let the coordinates of point P be `(x,y)`.
Suppose coordinates of point A are `(x_(1),y_(1))` and B are `(x_(2),y_(2))` then `x_(1)=-1,y_(1)=7,x_(2)=4` and `y_(2)=83`.
P divides AB in the ratio `2:3`.
`:.m:n=2:3`
By section formula
`x=(mx_(2)+nx_(1))/(m+n), y=(my_(2)+ny_(1))/(m+n)`
`:.x=(2(4)+3(-1))/(2+3), :.y=(2(-3)+3(7))/(2+3)`
`:.x=(8-3)/5, :.y=(-6+21)/5`
`:.x=5/5, :.y=15/5`
`:.x=1, :.y=3`
`P(1,3)` divides the line segment joining the points `A(_1,7)` and `B(4,-3)` in the ratio `2:3`.