Question

Let 0 <a <$\frac{\pi}{2}$ be fixed angle. If P = (cosq, sin q) &

Q = {cos (a –q), sin (a –q)}, then Q is obtained from P by-

• A. Clockwise rotation around origin through an angle a
• B. Anticlockwise rotation around origin through an angle a
• C. Reflection in the line through origin with slope tan a
• D. Reflection in the line through origin with slope tan $\frac{\alpha}{2}$

Answer 1

Answer: (D)

Reflection in the line through origin with slope tan $\frac{\alpha}{2}$

Answer 2

\ Point Q is the reflection of point P w.r.t. line through origin

with slope tan $\left( \frac{\alpha}{2} \right)$