Q.
The point (4, 1) undergoes the following three transformations successively. (i) Reflection about the line y=x(II) Translation through a distance 2 units along the +ve direction of x-axis(iii) Rotation through an angle π4 about the origin in counter clock wise direction then the final position of the point is
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a
(12,72)
b
(−12,72)
c
(−12,−72)
d
(−12,2)
answer is B.
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Detailed Solution
Reflection about y=x is (1, 4)2 units along +ve direction of x−axis is (3, 4) and usingx'=xcosθ−ysinθ= 3 cosπ4-4sin π4=32-42=-12y'=xsinθ+ycosθ=3 sinπ4+4cosπ4=32+42=72
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