If the algebraic sum of the perpendiculars from the points `(2,0),(0,2),(1,1)` to a variable line be zero, then prove that line passes through a fixed-point whose coordinates are `(1,1)dot`

Explanation

Let the variable straight line be `ax+by+c=0 ...(1)`

given the algebraic sum of perpendiculars from `(2,0),(0,2) and (1,1)` is zero

So,
`=>|2xxa+bxx0+cxx1|/(sqrt(a^2+b^2))+|0xxa+bxx2+ccc1|/(sqrt(a^2+b^2))+|1xxa+bxx1+cxx1|/(sqrt(a^2+b^2))`


`=>(2a+c)/sqrt(a^2+b^2)+(2bc)/sqrt(a^2+b^2)+(a+b+c)/sqrt(a^2+b^2)=0`

`=>2a+c+2b+c+a+b+c=0`
`=>3a+3b+3c=0`

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