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Question

# Let the algebraic sum of the perpendicular distances from the points (2,0),(0,2) & (1,1) to a variable straight line be zero, then the line passes through a fixed point whose co-ordinates are

A
(1,1)
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B
(2,3)
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C
(35,35)
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D
None of these
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Solution

## The correct option is A (1,1)Let the variable straight line be ax+by+c=0 ...(1)where algebraic sum of perpendiculars from (2,0),(0,2) and (1,1) is zero∴2a+0+c√a2+b2+0+2b+c√a2+b2+a+b+c√a2+b2=0⇒3a+3b+3c=0⇒a+b+c=0From equation (1) and (2) ax+by+c=0 always passes through a fixed point (1,1).

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