L is a variable line such that the algebraic sum of the distances of the points (1,1) (2,0) and (0,2) from the line is equal to zero. The line L will always pass through

Options

A. 1,1
B. 2,1
C. 1,2
D. 2,2

Answer

A

Explanation

Let the equation of line be ax +by +c =0
The perpendicular distance from (1,1) (2,0) and (0,2) to the line ax + by + c=0 are
` p_(1) = (a+b+c)/(sqrt(a^(2)+b^(2)) , p_(2) = (2a+c)/(sqrt(a^(2) +b^(2))) and p_(3) = (2b +c)/(sqrt(a^(2) +b^(2))`
It is given that ` P_(1) + p_(2) + p_(3) =0`
`(a +b+c)/(sqrt(a^(2) +b^(2)) + (2a+c)/(sqrt(a^(2) +b^(2)) + (2b+c)/(sqrt(a^(2) +b^(2)) = 0`
` Rightarrow 3a+3b +3c =0`
` Rightarrow ` a+b+c =0
From (Eq , (ii) it is clear that the line (i) passes through (1,1)