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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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