Question

# Let the algebraic sum of the perpendicular distance from the points (2,0), (0,2), and (1, 1) to a variable straight line be zero. Then the line passes through a fixed point whose coordinate are ___

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

## The correct option is B (1,1)Let the variable line be ax+by+c=0 ...(i) Then the perpendicular distance of the line from (2,0) is p1=2a+c√a2+b2 The perpendicular distance of the line from (0,2) is p2=2b+c√a2+b2 The perpendicaler distance of the line from (1,1) is p3=a+b+c√a2+b2 According to question, p1+p2+p3=0or 2a+c+2b+c+a+b+c√a2+b2=0or 3a+3b+3c=0ora+b+c=0 ...(ii) Form (i) and (ii) we can say that variable line (i) passes through the fixed point (1,1).

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