Q45 / 105 · JEE Main 2008 · Mathematics

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

  • A
    1
  • B
    2
  • C
    $-2$
  • Correct answer
    D
    $-4$

Solution

Slope of bisector $=k-1$ Middle point $=\left(\frac{\mathrm{k}+1}{2}, \frac{7}{2}\right)$ Equation of bisector is $y-\frac{7}{2}=(k-1)\left(x-\frac{(k+1)}{2}\right)$ Put $\mathrm{x}=0$ and $\mathrm{y}=-4$ $$ \Rightarrow k=\pm 4 $$

Hence, the correct answer is option: 'D'.

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