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Question

Let the equations of the perpendicular bisectors of AB and AC in a traingle ABC is x+y=2 and 2xy=10 respectively. If the coordinates of the point A(0,10), then the equation of the line BC is

A
y=2
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B
x+2y=20
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C
x+y=2
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D
x+y=6
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Solution

The correct option is A y=2
Let the coordinate of B(x1,y1) and C(x2,y2)
As x+y2=0 is perpendicular bisector of AB, B is the image of A about the line x+y2=0
For B
x101=y1101=2(0+102)2
x1=8; y1=2B(8,2)
For C
x202=y2101=2(01010)5
x2=16; y2=2C(16,2)
BC:y=2

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