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

To determine the equation of the bisectors of the angles between the lines \(|x| = |y|\), we need to analyze the given lines and find their angle bisectors.

The equations \(|x| = |y|\) represent two lines: \(x = y\) and \(x = -y\).

These lines intersect at the origin (0, 0) and form four angles in the coordinate plane. The angle bisectors of these lines will also intersect at the origin.

Let's find the angle bisectors:

1. The angle bisector of the acute angle between \(x = y\) and \(x = -y\) is the line \(y = 0\). This bisector is horizontal and passes through the origin.
2. The angle bisector of the obtuse angle (the supplementary angle) formed by these lines is \(x = 0\). This bisector is vertical and also passes through the origin.

Therefore, the equations of the angle bisectors are \(y = 0\) and \(x = 0\).

Among the given options, the correct answer is \(y = 0\) and \(x = 0\).