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The perpendicular bisector of the line s...

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

Text Solution

Verified by Experts

The correct Answer is:
B
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`
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