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Question

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 positive direction of x-axis.
(III) Rotation of coordinate axes through an angle π4 about the origin in the clockwise direction.
The final position of the point is given by the coordinates

A
(12,72)
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B
(2,72)
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C
(12,72)
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D
(2,72)
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Solution

The correct option is B (12,72)
Let B,C,D be the position of point A(4,1) after the three operations I, II and III respectively.
Then, B is (1,4), C is (1+2,4)=(3,4).
The point D is obtained from V by rotating the coordinate aces through an angle π4 in the anticlockwise direction.
Therefore, the coordinate of D is given by
X=3cosπ44sinπ4=12Y=3sinπ4+4cosπ4=72
Therefore coordinates of D are (12,72)

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