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