Explanation

(a)
Let the equation of line be
$ax + by + c = 0$ …(i)
The perpendicular distance from (1, 1), (2, 0) and (0, 2) to the line $ax + by + c = 0$ are
$p_{1} = \frac{a + b + c}{\sqrt{a^{2} + b^{2}}},\ p_{2} = \frac{2a + c}{\sqrt{a^{2} + b^{2}}},\ p_{3} = \frac{2b + c}{\sqrt{a^{2} + b^{2}}}$
Since, it is given that $p_{1} + p_{2} + p_{3} = 0$
$\Rightarrow \frac{a + b + c}{\sqrt{a^{2} + b^{2}}} + \frac{2a + c}{\sqrt{a^{2} + b^{2}}} + \frac{2b + c}{a^{2} + b^{2}} = 0$
$\Rightarrow 3a + 3b + 3c = 0$
$\Rightarrow a + b + c$ …(ii)
From Eq. (ii), it is clear that the line (i) passes through (1, 1)