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

Options

A. `-2`
B. `-4`
C. 1
D. 2

Answer

B

Explanation

The coordinates of the mid-point of PQ are `((k+1)/(2),(7)/(2))` .
Slope of PQ `=(4-3)/(1-K)=(1)/(1-k)`
`therefore ` Slope of the perpendicular bisector of PQ is (k-1). The equation of the perpendicular bisector of PQ, is
`y-(7)/(2)=(k-1)(x-(k+1)/(2))`
It passes through (0,-4)
`therefore -(15)/(2)=-((k^(2)-1))/(2) implies k=pm4`