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AP EAMCET2002MathematicsStraight Lines

If the axes are rotated through an angle 45^ in the positive direction without changing the origin, then the co-ordinates of the point ( 2 , 4) in the old system are

Options

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

Correct answer

A. (1-2 2 , 1+2 2 )

Step-by-step solution

If is the angle of rotation, then the co-ordinates in the new system are x^ =x +y , y^ =y -x Given that x^ = 2 , y^ =4 Thus, x +y = 2 y -x =4 Also, = 4 x 4 +y 4 = 2 and y 4 -x 4 =4 array ll & x+y=2 and & y-x=4 2 array On adding Eqs. (i) and (ii), we get 2 y=2+4 2 y=1+2 2 On subtracting (i) and (ii), we get array rlrl & & 2 x & =2-4 2 & x & =1-2 2 array x=1-2 2 Thus, the co-ordinates of ( 2 , 4) in the old system (1-2 2 , 1+2 2 )

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