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Question

The perpendicular bisector of the line segment doing the points P(1,4) & Q(K,3) has Y-intercept −4, then a possible value of k is

A
2
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B
2
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C
4
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D
1
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Solution

The correct option is B 4
Line segment PQ has slope,m
m=431k=11k

Line segment PQ has midpoint
(1+k2,4+32)=(1+k2,72)
Perpendicular bisector has slope (1k)1=k1 and passes through point (1+k2,72)
Equation of perpendicular bisector:

y72=(k1)(x(1+k)2)

y=(k1)x(k1)(1+k)2+72

y=(k1)x+(1k)(1+k)+72

y=(k1)x+1k²+72

y=(k1)x+8k²2
Perpendicular bisector has y-intercept =4

8k²2=4

8k2=8
k2=16 k=±4

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