Question

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. $-2$
• B. $-4$
• C. $1$
• D. $2$

Answer 1

The correct option is B $-4$

Slope of PQ=$\frac{3-4}{k-1}=\frac{-1}{k-1}$

slope of the perpendicular bisector of $PQ=(k-1)$

Also midpoint of PQ=$(\frac{k+1}{2},\frac{7}{2})$

Equation of perpendicular bisector of $PQ$ is $y-\frac{7}{2}=(k-1)(x-\frac{k+1}{2})$

$\Rightarrow 2y-7=2x(k-1)-(k^2-1)$

$\Rightarrow 2(k-1)x-2y+(8-k^2)$

$Y$-intercept is, $\frac{8-k^2}{2}=-4=k=\pm 4$