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AP EAMCET2003MathematicsStraight Lines

The co-ordinate axes are rotated through an angle 135^ . If the co-ordinates of a point P in the new system are known to be (4,-3) , then the co-ordinates of P in the original system are

Options

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

Correct answer

D. (- 1 2 , 7 2 )

Step-by-step solution

Let (x₁, y₁ ) be the co-ordinate of new system, then x₁=x +y ₁=-x +y Given that (x₁, y₁ )=(4,-3) and =135^ 4=x 135^ +y 135^ 4=- x 2 + y 2 ( i )-3=-x 135^ +y 135^ -3=- x 2 - y 2 ( ii ) On adding Eqs. (i) and (ii), we get 1=- 2 x 2 x=- 1 2 On subtracting Eqs. (i) and (ii), we get 7= 2 y 2 y= 7 2 Thus (x, y)= (- 1 2 , 7 2 )

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