The coordinates of the foot of the perpendicular drawn from the point (3,4) on the line 2x +y-7 =0 are

Options

A. `9/5, 17/5`
B. 1,5
C. `-5,1`
D. 1,-5

Answer

A

Explanation

Here , ` (x_(1) ,y_(1)) = 3,4`

Given equation is 2x + y-7=0
On comparing with ax + by +c =0 we get a =2 , b =1 and c=-7
Let (h,k) be the coordinates of the foot ,
Then , ` (h-3)/2 = (k-4)/1 `
` (-(2xx 3 + 1 xx 4 -7))/(2^(2) +1^(2)) = (-3)/5`
` Rightarrow (h-3)/2 = (-3)/5`
`and (k-4)/1 = (-3)/5`
` Rightarrow h= (-6)/5 + 3 `
` and k = (-3)/5 + 4`
`Rightarrow h = 9/5`
` and k = 17/5`