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AP EAMCET202119 Aug 2021Evening ShiftMathematicsStraight LinesActual

When the coordinate axes are rotated through an angle 135 ° , the coordinates of a point P in the new system are known to be ( 4 , - 3 ) . Then find the coordinates of P in the original system.

Options

  1. A1 2 , 7 2
  2. B− 1 2 , 7 2
  3. C1 2 , − 7 2
  4. D− 1 2 , − 7 2

Correct answer

B. − 1 2 , 7 2

Step-by-step solution

Let, we have a point P x ,   y , Now, the coordinate axes rotated through an angle 135 ° , and the coordinate of the point P in new system is 4 ,   - 3 . Hence, applying the formula, the coordinates of the point P in the original system is x = x ' cos θ - y ' sin θ = 4 cos 135 ° - - 3 sin 135 ° = - 4 2 + 3 2 = - 1 2 Similarly, y = x ' sin θ + y ' cos θ = 4 sin 135 ° + - 3 cos 135 ° = 4 2 + 3 2 = 7 2 where, x ,   y is the coordinate of origi

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