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AP EAMCET201822 Apr 2018Morning ShiftMathematicsStraight LinesActual

If the coordinates of a point P changes to (2,-6) when the coordinate axes are rotated through an angle of 135^ , then the coordinates of P in the original system are

Options

  1. A(-2,6)
  2. B(-62)
  3. C(2 2 , 4 2 )
  4. D( 2 ,- 2 )

Correct answer

C. (2 2 , 4 2 )

Step-by-step solution

If (x, y) is old coordinates and (X, Y) are new coordinates, when axes are rotated through an angle of , then aligned & x=X -Y and y=X +Y & x=2 135^ -(-6) 135^ & and y=2 135^ +(-6) 135^ & x=2 ( -1 2 )+6 ( 1 2 ) and y=2 ( 1 2 )-6 ( -1 2 ) & x= 4 2 and y= 8 2 & x=2 2 and y=4 2 . aligned Coordinates of P in the original system are (2 2 , 4 2 ) .

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