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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 2x−y=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=2Let the coordinate of B≡(x1,y1) and C≡(x2,y2) As x+y−2=0 is perpendicular bisector of AB, B is the image of A about the line x+y−2=0 For B ⇒x1−01=y1−101=−2(0+10−2)2 ⇒x1=−8; y1=2∴B≡(−8,2) For C ⇒x2−02=y2−10−1=−2(0−10−10)5 ⇒x2=16; y2=2∴C≡(16,2) ⇒BC:y=2

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