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Manipal MET2011MathematicsStraight Lines

The line x+2 y=4 is translated parallel to itself by 3 unit in the sense of increasing x and then rotated by 30^ in the anti-clockwise direction about the point where the shifted line cuts the x -axis. The equation of the line in the new position is

Options

  1. Ay= ( -30^ )(x-4-3 5 )
  2. By= (30^ - )(x-4-3 5 )
  3. Cy= ( +30^ )(x+4+3 5 )
  4. Dy= ( -30^ )(x+4+3 5 )

Correct answer

A. y= ( -30^ )(x-4-3 5 )

Step-by-step solution

The equation of a line parallel to x+2 y=4 is x+2 y=k . Since, the distance between these two lines is 3 , therefore array ll & k 1+4 - 4 1+4 =3 & k=4+3 5 array This shifted line cuts x -axis at (k, 0) . After rotation the slope of the line is ( -30^ ) , where = (slope of (x+2 y=4)=- 1 2 The equation of the line in the new position is aligned & y-0= ( -30^ )(x-k) & y= ( -30^ )(x-k) aligned where k=4+3 5

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