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Question

# If the algebraic sum of the perpendiculars drawn from the points (2,0),(0,2),(1,1) to a variable line is zero, then the line will always pass through a fixed point whose co-ordinates are

A
(1,1)
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B
(2,2)
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C
(3,3)
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D
(0,0)
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Solution

## The correct option is A (1,1)Let the variable line be ax+by=1 ...(1) If it is given that the algebraic sum of perpendiculars drawn from the points (2,0),(0,2),(1,1) is zero. ∴2a−1√a2+b2+2b−1√a2+b2+a+b−1√a2+b2=0 ⇒3a+3b−3=0 ⇒a+b=1 ...(2) Comparing (1) and (2), we get (x,y)=(1,1) So, variable line always passes through fixed point (1,1)

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