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Question

The point (4, 1) undergoes the following transformation successively.
(i) reflection about the line y = x
(ii) translation through a distance 2 units along the positive direction of x - axis
(iii) rotation through an angle π4 about the origin in the anticlockwise direction.
(iv) reflection aout x = 0
The final position of the given point is


A

(12, 72)

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B

(12, 72)

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C

(12, 72)

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D

(12 72)

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Solution

The correct option is C

(12, 72)


Let B, C, D, E be the positions of the given point A(4, 1) after the transformation (i), (ii), (iii) and (iv) successively.

The coordinates of B are (1, 4) and that of C are (1 + 2, 4 + 0), i.e., (3, 4). Now if OC makes an angle θ with x - axis, OD makes and an angle θ+π4 with x - axis. If (h, k) denote the coordinates of D, then
h=OD cos (θ+45), k=sin (θ+45)
and OD = OC = 5, sin θ=45, cos θ=35
h=(52) (cos θsin θ)=12k=(52)(cos θ+sin θ)=72
coordinates of D are (12, 72) and its reflection about x = 0 in (12, 72)


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