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NTA Abhyas JEE Main2020MathematicsStraight LinesPractice

The perpendicular bisector of the line segment joining A 1 , 4 and B t , 3 has y -intercept equal to - 4 . Then, the product of all possible values of t is equal to

Options

  1. A1
  2. B2
  3. C- 16
  4. D- 4

Correct answer

C. - 16

Step-by-step solution

The slope of the perpendicular bisector = t - 1 The mid-point of the line segment = t + 1 2 , 7 2 ∴ Equation of the bisector is y - 7 2 = t - 1 x - t + 1 2 Putting x = 0 and y = - 4 , we get, t = ± 4 Hence, the required product = 4 - 4 = - 16

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