If the perpendicular bisector of the line segment

Question:

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 :-

 

  1. $\sqrt{15}$

  2. $-2$

  3. $\sqrt{14}$

  4. $-4$


Correct Option: , 4

Solution:

Slope $=\mathrm{m}=\frac{1}{1-\mathrm{k}}$

Equation of $\perp^{\mathrm{r}}$ bisector is

$y+4=(k-1)(x-0)$

$\Rightarrow \mathrm{y}+4=\mathrm{x}(\mathrm{k}-1)$

$\Rightarrow \frac{7}{2}+4=\frac{\mathrm{k}+1}{2}(\mathrm{k}-1)$

$\Rightarrow \frac{15}{2}=\frac{\mathrm{k}^{2}-1}{2} \Rightarrow \mathrm{k}^{2}=16 \Rightarrow \mathrm{k}=4,-4$

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