Find the co-ordinates of the foot of perpendicular drawn from the point `(3,-3)` to the line `x-2y=4`.

Explanation

Let the line `x-2y=4` be `AB` and `CD` is perpendicular from point `C(3,-3)AB`.
Now, for the slope of `AB`
`2y=x-4`
`implies y=(1)/(2)x-2`
`:.` Slope of `AB`
`m_(1)=(1)/(2)`
Slope of perpendicular line `CD`
`m_(2)=-(1)/(m_(1))=-2`
Equation of `CD`
`(-y-3)=-2(x-3)`
`implies y+3=-2x+6`
`implies 2x+y=3`
On solving the equation of `CD` and equation of `AB`, `x=2`, `y=-1`
`:.` Co-ordinates of foot of perpendicular `D=(2,-1)`