Thank you for reporting, we will resolve it shortly
Q.
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 :-
Slope $= m =\frac{1}{1- k }$
Equation of $\perp^{ r }$ bisector is
$y+4=(k-1)(x-0)$
$\Rightarrow y+4=x(k-1)$
$\Rightarrow \frac{7}{2}+4=\frac{ k +1}{2}( k -1)$
$\Rightarrow \frac{15}{2}=\frac{ k ^{2}-1}{2} \Rightarrow k ^{2}=16 \Rightarrow k =4,-4$
