Question

find the equation of line perpendicular to line x-4y+3=0 which makes an intercept of length 2 units on x-axis (I have found the equation as x=1.is it coerrect or not correct)

Answer 1

Dear Student,

Given line: x - 4y + 3 = 0
$\Rightarrow$4y = x + 3
$\Rightarrow$y = $\frac{\mathrm{x}}{4}+\frac{3}{4}$
Comparing it with : y = mx + c
Slope of line (m) = $\frac{1}{4}$
Now, let the slope of perpendicular line be n, therefore
$\Rightarrow$m * n = - 1
$\Rightarrow$n = $\frac{-1}{\mathrm{m}}$
$\Rightarrow$n = - 4
Let the equation of line be y = nx + c
$\Rightarrow$y = - 4x + c
When y = 0, x = 2
$\Rightarrow$0 = - 4(2) + c
$\Rightarrow$c = 8
Therefore, equation of line is: y = - 4x + 8

Regards