Let 0 < < 2 be a fixed angle. If P = ( , ) and Q = ( ( - ), ( - ) ) then Q is obtained from P by

JEE Advanced Mathematics question

Let be a fixed angle. If and then is obtained from by

(A)clockwise rotation around origin through an angle
(B)anticlockwise rotation around origin through an angle
(C)reflection in the line through origin with slope
(D)reflection in the line through origin with slope Correct

Answer: (D)

Solution

and are on the unit circle at polar angles and . Reflection in the line through at angle sends polar angle to . With , we get , exactly . So is the mirror image of in $y =

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Question ID VK-110595