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AP EAMCET2013MathematicsStraight Lines

The origin is translated to (1,2) . The point (7,5) in the old system undergoes the following transformations successively. I. Moves to the new point under the given translation of origin. II. Translated through 2 units along the negative direction of the new X -axis. III. Rotated through an angle 4 about the origin of new system in the clockwise direction. The final position of the point (7,5) is

Options

  1. A( 9 2 , -1 2 )
  2. B( 7 2 , 1 2 )
  3. C( 7 2 , -1 2 )
  4. D( 5 2 , -1 2 )

Correct answer

C. ( 7 2 , -1 2 )

Step-by-step solution

Under the translation of origin to (1,2) the point (7,5) undergoes to (7-1,5-2) (6,3) Under the translation through 2 units along the negative direction of the new x -axis, the point (6,3) undergoes to (6-2,3) (4,3) Under the rotation throw an angle 4 about the origin of new system in the clockwise direction, the final position of point (7,5) aligned & = (4 4 +3 4 ,-4 4 +3 4 ) & = ( 4 2 + 3 2 ,- 4 2 + 3 2 )= ( 7 2 ,- 1 2 ) aligned

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