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Question

Find the equation of the right bisector of the line segment joining the points (3,4) and (1,2).

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Solution

The right bisector of a line segment bisects the line segment at 90.

The end-points of the line segment are given as A(3,4) and B(1,2).
Accordingly, mid-point of AB ={312,4+22}=(1,3)
and slope of AB =2413=24=12
slope of line perpendicular to AB =1{12}=2
Thus equation of the line passing through (1,3) and having a slope of 2 is given by,
(y3)=2(x1)
y3=2x+22x+y=5
Thus, the required equation of the line is 2x+y=5.

387484_419926_ans_54b66ea0dc7243e79933f29c265ce41f.png

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