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 coordinates are___

Options

A. `(-1,1)`
B. `(1,1)`
C. `(1,-1)`
D. `(-1,-1)`

Answer

B

Explanation

Let the equation of the line be `ax + by + c =0`
Then, according to the given condition, we have
`(2a + 0b + c)/(sqrt(a^(2) +b^(2)))+(0+2b +c)/(sqrt(a^(2)+b))+(a+b+c)/(sqrt(a^(2)+b^(2))) =0`
`rArr 3a + 3b + 3c =0 rArr a+b + c=0`
This shows that `ax + by + c=0` passes through the fixed point (1,1).