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Find the coordinates of the foot of perp...

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

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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))`
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