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AP EAMCET202022 Sep 2020Evening ShiftMathematicsStraight LinesActual

Find the coordinates of M in the original system if the point M changes to (4,-3) when the axes are rotated through an angle of 135^ .

Options

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

Correct answer

C. ( -1 2 , 1 2 )

Step-by-step solution

aligned (*) Let M^ =(4,-3) & = (x^ , y^ ) & =135^ aligned Let coordinates of M be (x, y) we have, aligned x & =x^ -y^ and y=x^ +y^ x & =4 135+3 135^ and y & =4 135^ +(-3) 135^ x & =4 ( -1 2 )+3 ( 1 2 ) and y & =4 1 2 +(-3) 1 2 x & =- 1 2 and y= 1 2 M & =(x, y)= ( -1 2 , 1 2 ) aligned (*) No option is correct.

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