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Math Help - Reflection in y=xtan{theta}

  1. #1
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    Reflection in y=xtan{theta}

    Find the reflections of i and j in the line y=x\tan\theta

    I don't know where to begin. i and j are the position vectors of (1,0) and (0,1) respectively. Since y=x\tan\thetacan be any line passing through the origin, how am i supposed the find the perpendicular distance between the point and line?
    Thanks
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  2. #2
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    Quote Originally Posted by arze View Post
    Find the reflections of i and j in the line y=x\tan\theta

    I don't know where to begin. i and j are the position vectors of (1,0) and (0,1) respectively. Since y=x\tan\thetacan be any line passing through the origin, how am i supposed the find the perpendicular distance between the point and line?
    Thanks
    The line passing through image of i will make an angle 2θ with the x-axis.
    So the coordinates of the image is (cos2θ , sin2θ ). In terms of tan θ it can be given as [ (1-tan^2θ)/(1+tan^2θ), 2tanθ/(1+tan^2θ) ]
    Similarly you can find the image of j.
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