Find coordinates of the foot of perpendicular, image and equation of perpendicular drawn from the point `(2, 3)` to the line `y = 3x-4. `

Options

A. `((37)/(10),(-1)/(10))`
B. `(-(1)/(10),(37)/(10))`
C. `((10)/(37),-10)`
D. `((2)/(3),(1)/(3))`

Answer

B

Explanation

Given equation of the line is `y=3x+4`
`therefore` Slope of line,`m_1=3`
So, the slope of line OP is`-(1)/(3)` , `[because OPpmAB]`

`therefore` Equation of line OP is `y-3=-(1)/(3)(x-2)`
`rArr3y-9=-x+2`
`rArrx+3y-11=0`
Using the value of y from Eq. (i) in Eq.(ii), we get
`x+3(3x+4)-11=0`
`rArrx+9x+12-11=0`
`rArr10x+1=0rArrx=-(1)/(10)`
Put `x=(-1)/(10)` in Eq.(i), we get
`y=(-3)/(10)+4=(-3+40)/(10)=(37)/(10)`
So, the foot of perperdicular is `(-(1)/(10),(37)/(10))`.