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 :-

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 :- (A) √15 (B) -2 (C) √14 (D) -4

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/6b5429de2cbddf512717057f24139149-.png" /> Slope = m =(1/1- k ) Equation of perp r bisector is y+4=(k-1)(x-0) ⇒ y+4=x(k-1) ⇒ (7/2)+4=( k +1/2)( k -1) ⇒ (15/2)=( k 2-1/2) ⇒ k 2=16 ⇒ k =4,-4

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 :-

$15$

$- 2$

$14$

$- 4$

Slope $= m = \frac{1}{1 - k}$
Equation of $⊥^{r}$ bisector is
$y + 4 = (k - 1) (x - 0)$
$\Rightarrow y + 4 = x (k - 1)$
$\Rightarrow \frac{7}{2} + 4 = \frac{k + 1}{2} (k - 1)$
$\Rightarrow \frac{15}{2} = \frac{k ^{2} - 1}{2} \Rightarrow k^{2} = 16 \Rightarrow k = 4, - 4$

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 :-

15​

−2

14​

−4