The perpendicular bisector of the line segment joining P (1, 4) and Q (k, 3) has y-intercept `-4` . Then a possible value of k is (1) 1 (2) 2 (3) `-2` (4) `-4`

Explanation

if two lines are `_|_` then

`m_1 * m_2 = -1`

`m_2 = (4-3)/(1-k) = 1/(1-k)`

`AB _|_ PQ`

`m_1 * m_2 = -1`

`m_1 = -1/m_2 = k-1`

`C= ((1+k)/2, (4+3)/2) = ((1+k)/2, 7/2)`

eqn of line AB is `(y- 7/2)/(x - ((1+k)/2))= k-1`

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