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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-

A
1
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B
2
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C
2
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D
4
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Solution

The correct option is D 4
Given,

co-ordinates P(1,4) and Q(k,3)

perpendicular bisector has a y-intercept of 4 units

the coordinate at that point will be (0,4)

let, M be the point where the perp. bisects the line

So, M is the midpoint
co-ordinate of M is (k+12,72)

SlopeofPQ=431k

=(11k)=m1 (let)

m1=1m2

m2=1m1=111k=(k1)

Slopeofline=m2=(k1)

(y72)=(k1)(xk+12)

152=(k+1)(k1)2.....(putting x=0 and y=4 and simplifying)

k21=15

k2=16

k=±4
So, one of the possible value is 4
hence, Option D is the answer.

1239100_1321149_ans_935abd570e87475bb1828057b5ef9d10.png

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