Question

if line y – x + 2 = 0 is shifted parallel to itself towards the positive direction of the x- axis by a perpendicular distance of 3root2 units ,then the equation of the new line is what?

Answer 1

$$\begin{gathered} \mathrm{Given}\mathrm{line}:-\mathrm{y}-\mathrm{x}+2=0 \\ \mathrm{line}\mathrm{parallel}\mathrm{to}\mathrm{y}-\mathrm{x}+2=0\mathrm{is} \\ \mathrm{y}-\mathrm{x}+\mathrm{c}=0 \\ \mathrm{distance}\mathrm{between}\mathrm{these}\mathrm{two}\mathrm{lines}=3\sqrt{2} \\ \mathrm{distance},\mathrm{d}=\frac{\left|{\mathrm{c}}_2-{\mathrm{c}}_1\right|}{\sqrt{{\mathrm{a}}^2+{\mathrm{b}}^2}} \\ \mathrm{so}, \\ 3\sqrt{2}=\frac{\left|\mathrm{c}-2\right|}{\sqrt{{\left(-1\right)}^2+{\left(1\right)}^2}} \\ 3\sqrt{2}=\frac{\left|\mathrm{c}-2\right|}{\sqrt{2}} \\ \Rightarrow \left|\mathrm{c}-2\right|=6 \\ \mathrm{so},\mathrm{c}-2=6\left(\mathrm{since}\mathrm{line}\mathrm{is}\mathrm{shifted}\mathrm{towards}\mathrm{positive}\mathrm{x}-\mathrm{axis}\right) \\ \mathrm{c}=8 \\ \mathrm{Equation}\mathrm{of}\mathrm{new}\mathrm{line}\mathrm{is}\mathrm{y}-\mathrm{x}+8=0\mathrm{ANS}... \end{gathered}$$