JEE Main20204 Sep 2020Evening ShiftMathematicsStraight LinesActual

If the perpendicular bisector of the line segment joining the points P ( 1 , 4 ) and Q ( k , 3 ) has y -intercept equal to - 4 , then a value of k is;

Options

A- 2
B- 4
C14
D15

Correct answer

B. - 4

Step-by-step solution

Mid point of PQ is k + 1 2 , 7 2 And slope of PQ = 1 1 - k So equation of perpendicular bisector of PQ y - 7 2 = ( k - 1 ) x - k + 1 2 It's y intercept = - 4 . So, this equation must satisfy 0 , - 4 . ⇒ - 15 2 = - k 2 - 1 2 k 2 = 16 ⇒ k = ± 4

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