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AP EAMCET201921 Apr 2019Evening ShiftMathematicsStraight LinesActual

If the perpendicular bisector of the line segment joining A ( α , 3 ) and B ( 2 , - 1 ) has y -intercept 1 , then α =

Options

  1. A0
  2. B± 1
  3. C± 2
  4. D± 3

Correct answer

C. ± 2

Step-by-step solution

Consider the equation of perpendicular bisector is y = m   x + c The intercept is 1 , thus the equation becomes y = m   x + 1   The mid-point of the points A ( α , 3 ) and B ( 2 , - 1 ) is α + 2 2 , 1 Since the equation passes through α + 2 2 , 1 Thus, 1 = m α + 2 2 + 1 2 = m ( α + 2 ) + 2 m ( α + 2 ) = 0 m α + 2 m = 0   … I Here, m is the gradient of the perpendicular line. m = - α - 2 4 Substitute the value in equation ( I ) . α 2 - α 4 +

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