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Q.

The point (3,2) undergoes the following three transformations in the order given
i) Reflection about the line y = x
ii) Translation by the distance 1 unit in the positive direction of x – axis
iii) Rotation by an angle $π / 4$ about the origin in the anticlockwise direction Then the final position of the point is

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a

$(0, 3)$

b

$(- 2, 3)$

c

$(0, \sqrt{18})$

d

$(- \sqrt{18}, \sqrt{18})$

answer is C.

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Detailed Solution

Reflection of (3, 2) about y=x is (2, 3)
If the point (2, 3) is translated through distance 1 unit in the positive direction of x-axis, then the coordinates of the point are (3, 3). After the rotation through an angle $π / 4$ in anticlockwise direction, the point is $(0, \sqrt{18})$

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