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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+ca2+b2
The perpendicular distance of the line from (0,2) is
p2=2b+ca2+b2
The perpendicaler distance of the line from (1,1) is
p3=a+b+ca2+b2
According to question,
p1+p2+p3=0or 2a+c+2b+c+a+b+ca2+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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