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AP EAMCET202017 Sep 2020Evening ShiftMathematicsStraight LinesActual

If the axes are rotated through an angle (45^ ), then the co-ordinates of the point ((4 2 ,-6 2 ) ) in the new system are ____

Options

  1. A((-10,-2) )
  2. B((-2,-10) )
  3. C((10,10) )
  4. D((-2,10) )

Correct answer

B. ((-2,-10) )

Step-by-step solution

Let ((x, y) ) are coordinates related to old axes and ((X, Y) ) are related to rotated (new) axes then, ( gathered x=X -Y y=X +Y gathered ) Here, ( aligned & =45^ & x=4 2 , y=-6 2 aligned ) So, ( 4 2 = X 2 - Y 2 ) and (-6 2 = X 2 + Y 2 ) Adding we have, (-2 2 =2 X 2 X=-2 ) and subtracting, (10 2 =- 2 Y 2 Y=-10 . )

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