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\[\left( -\frac{1}{\sqrt{2}},\frac{7}{\sqrt{2}} \right)\].You need to login to perform this action.
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