Thread: Reflection in y=xtan{theta}

1. 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 $y=x\tan\theta$can be any line passing through the origin, how am i supposed the find the perpendicular distance between the point and line?
Thanks

2. Originally Posted by arze
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 $y=x\tan\theta$can 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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y equals xtantheta

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