1.

Let the algebraic sum of the perpendicular distances from the points `(2,0),(0,2)a n d(1,1)`to a variable straight line be zero. Then the line pass through a fixedpoint whose coordinates are`(1,1)`b. `(2,2)`c. `(3,3)`d. `(4,4)`A. `(-1,1)`B. `(1,1)`C. `(1,-1)`D. `(-1,-1)`

Answer» Correct Answer - B
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).


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