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CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2006

  • question_answer
    The point (4, 1) undergoes the following three transformations successively: (i) reflection about the line\[y=x\] (ii) translation through a distance of 2 unit along the positive direction of\[x-\]axis (iii) rotation through an angle of\[\frac{\pi }{4}\]about the origin in the anticlockwise direction The final position of the point is:

    A)  \[\left( \frac{1}{\sqrt{2}},\frac{7}{\sqrt{2}} \right)\]                       

    B)  \[\left( -\frac{1}{\sqrt{2}},\frac{7}{\sqrt{2}} \right)\]

    C)  \[(-\sqrt{2},7\sqrt{2})\]               

    D)         \[(\sqrt{2},7\sqrt{2})\]

    E)  \[(\sqrt{2},-7\sqrt{2})\]

    Correct Answer: B

    Solution :

    Let\[z=4+i\]when reflected along\[y=x\]will become\[z=1+4i\] When translated by 2 unit\[z=3+4i.\] When rotated by angle\[\pi /4\]in anticlockwise direction will give \[z=(3+4i)\left( \cos \frac{\pi }{4}+i\sin \frac{\pi }{4} \right)\] \[z=\frac{1}{\sqrt{2}}[3-4+i(3+4)]=-\frac{1}{\sqrt{2}}+i\frac{7}{\sqrt{2}}\] \[\therefore \]Required point is\[\left( -\frac{1}{\sqrt{2}},\frac{7}{\sqrt{2}} \right)\].


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