IIT JEE Entrance Exam
The equation of the line segment AB is y = x. If A and B lie on the same side of the line mirror 2x – y = 1, the image of AB has the equation 
Options
x + y = 28x + y = 9
7x – y = 6
None of these
x + y = 28x + y = 97x – y = 6None of these
1 Answer
Alekhya goud
The answer is #3: 7x - y = 6.
The condition implies that the mirror m: 2x - y = 1 (slope 2) is an angle bisector of the angle between the line AB: y = x (slope 1) and its image - the line A'B': y = kx + n (coefficients k and n to be determined), or
∡(AB, m) = ∡(m, A'B') /in that order - both angles to be measured counterclockwise!/
Now using the slopes
The condition implies that the mirror m: 2x - y = 1 (slope 2) is an angle bisector of the angle between the line AB: y = x (slope 1) and its image - the line A'B': y = kx + n (coefficients k and n to be determined), or
∡(AB, m) = ∡(m, A'B') /in that order - both angles to be measured counterclockwise!/
Now using the slopes
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