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Question

# The equation two the perpendicular bisectors of the line segment joining (1,2),(3,4) is

A
2xy+5=
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B
x+y5=0
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C
3x2y+5=0
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D
x+y4=0
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Solution

## The correct option is B x+y−5=0Slope of the line joining the points (1,2) and (3,4)-m1=y2−y1x2−x1=4−23−1=22=1Therefore,m1m2=−1⇒m2=−1m1=−1Also mid-point of the line joining the points (1,2) and (3,4)-(h,k)=(3+12,4+22)=(2,3).Therefore,Equation of perpendicular bisector =(y−k)=m2(x−h)=y−3=−1(x−2)=y−3=2−x=x+y−5=0Hence the equation of prpendicular bisector is x+y−5=0.

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