Question

The equation of bisectors of the angles between the lines \(|x| = |y|\) are

• A. \(y = \pm x\) and \(x = 0\)
• B. \(x = 1/2\) and \(y = 1/2\)
• C. \(y = 0\) and \(x = 0\)
• D. None of the above

Hint:

Angle bisectors of \(x \pm y = 0\) are the coordinate axes.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Lines are \(x + y = 0\) and \(x - y = 0\).
Step 2: Detailed Explanation:
Bisectors: \(\frac{x + y}{\sqrt{2}} = \pm \frac{x - y}{\sqrt{2}}\)
Taking \(+\): \(y = 0\), Taking \(-\): \(x = 0\)
Step 3: Final Answer:
Bisectors are \(x = 0\) and \(y = 0\).