A line intersects the straight lines `5x-y-4=0` and `3x-4y-4=0` at `A` and `B` , respectively. If a point `P(1,5)` on the line `A B` is such that `A P: P B=2:1` (internally), find point `Adot`

Answer

(75/17, 307/17)

Explanation

Any point A on the first line is (t, 5t-4). Any point B on the second line is (r, (3r-4)/4). Hence,
`1=(2r+t)/(3) " and " 5=((3r-4)/(2)+5t-4)/(3)`
or 2r+t = 3 and 3r+10t = 42
On solving, we get
`t = (75)/(17)`
Hence, A is (75/17,307/17).