Find the distance of the point `(2,3)` from the lilne `2x-3y+9=0` measured along a line `x-y+1=0.`

Explanation

let `2x−3y+9=0` ……..(i),

`x−y+1=0` ………(ii)

solving (i) and (ii) we get `y=7 and x=6`

Point of intersection `(6,7)`

Distance between` (2,3)` and `(6,7)`

`=sqrt((6−2)^2+(7−3)^2)`

`​=4sqrt(2)units`