Q.

The point (7,5) undergoes the following transformations successivelyi) The origin is translated to (1,2)ii) Translated through 2 units along the negative direction of the new X-axisiii) Rotated through an angle π4 about the origin in the clockwise direction.The final position of the point (7,5) is

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a

92,−12

b

72,12

c

72,−12

d

(52,−12)

answer is C.

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Detailed Solution

After first transformation given point P (7,5) becomes Q (6,3) after second transformation Q (6,3) becomes to  (6-2,3) = R (4,3), OR=OR1=5,tanθ=34∴sinθ=35,cosθ=45 ∴The final position of the point=OR1cosθ−π4,OR1sinθ−π4                                                           =5·452+352,5·352-452
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The point (7,5) undergoes the following transformations successivelyi) The origin is translated to (1,2)ii) Translated through 2 units along the negative direction of the new X-axisiii) Rotated through an angle π4 about the origin in the clockwise direction.The final position of the point (7,5) is