Find the coordinates of the foot o the perpendicular from the point (-1, 3) to the line `3x-4y-16=0`

Explanation

Given line `3x-4y-16=0`…….`(1)`
Let the equation of its perpendicular line `PQ` is,
`4x+3y=lambda`……..`(2)`
This line passes through the point `(-1,3)`
`:. 4(-1)+3(3)=lambda`
`implies lambda=5`
From equation `(2)`,
`4x+3y=5`.......`(3)`
Solving equations and `(3)` , we get
`x=(68)/(25)` and `y=-(49)/(25)`
`:.` Coordinates of foot of perpendicular
`=((69)/(25),(-49)/(25))`