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​

Answer 1

Answer:

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

Slop of Perpendicular Bisector of PQ = (k - 1)

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

Equation of Perpendicular Bisector is

$y - \frac{7}{2} = (k - 1).(x - \frac{k + 1}{2} ) \\ \\ 2x - 7 = 2(k - 1) - ( {k}^{2} - 1) \\ \\ 2(k - 1)x - 2y + (8 - {k}^{2} ) = 0 \\ \\ y - intercept \: = \: \frac{ - 8 - {k}^{2} }{ - 2} = - 4 \\ \\ 8 - {k}^{2} = - 8 \\ \\ {k}^{2} = 16 \\ \\ k = ± 4$