Find an equation of the perpendicular bisector of ab

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Find the equation of the perpendicular bisector of AB where A and B are the points (3,6) and (-3,4) respectively. Also find its point of intersection with (i) x-axis and (ii) y-axis.

Answered by admin @


Given that A=(3,6) and B=(-3,4)
The equation of perpendicular bisector of AB is the locus of the points which are equidistant from A and B.
Let a point on the perpendicular bisector=P=(x,y)
PA=PB
PA²=PB²
(x-3)²+(y-6)²=(x+3)²+(y-4)²
x²+3²-2(3)(x)+y²+6²-2(6)(y)=x²+3²+2(3)(x)+y²+4²-2(y)(4)
9-6x+36-12y=9+6x+16-8y
12x+4y-20=0
4(3x+y-5)=0
3x+y-5=0
Hence 3x+y-5=0 is the equation of the perpendicular bisector of AB where A=(3,6) and B=(-3,4).


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