Question

If line $y-x+2=0$ is shifted parallel to itself towards the x-axis by a perpendicular distance of $3\sqrt{2}$ units, then the equation of the new line is may be-

• A. $y=x+4$
• B. $y=x+1$
• C. $y=x-(2+3\sqrt{2})$
• D. $y=x-8$

Answer 1

The correct option is D $y=x-8$

Given line: $y-x+2=0$

Line parallel to $y-x+2=0$ is $y-x+c=0$

Distance between these two lines $3\sqrt{2}$

Distance ,$d=\frac{|c_2-c_1|}{\sqrt{a^2+b^2}}$

So,

$3\sqrt{2}=\frac{|c-2|}{\sqrt{(-1{)}^2+(1{)}^2}}$

$3\sqrt{2}=\frac{|c-2|}{\sqrt{2}}$

$|c-2|=6$

So, $c-2=6$ [Since line is shifted towards positive x-axis]

$c=8$

Equation of new line is $y-x+8=0$ or $y=x-8$