Question

The distance between the parallel lines $y = x + 4$ and $y = x - 2$ is:

• A. $3\sqrt{2}$
• B. $\sqrt{2}$
• C. $2\sqrt{2}$
• D. $6$

Hint:

Always ensure the coefficients of $x$ and $y$ are identical in both equations before applying the formula.

Answer 1

The Correct Option is A

Step 1: Concept
For lines $Ax + By + C_{1} = 0$ and $Ax + By + C_{2} = 0$, distance $d = \frac{|C_{1} - C_{2}|}{\sqrt{A^{2} + B^{2}}}$.
Step 2: Analysis
Lines: $x - y + 4 = 0$ and $x - y - 2 = 0$. $d = \frac{|4 - (-2)|}{\sqrt{1^{2} + (-1)^{2}}} = \frac{6}{\sqrt{2}}$.
Step 3: Conclusion
$d = 3\sqrt{2}$.
Final Answer: (A)