Question

$L$ 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

• A. $(1,1)$
• B. $(2,1)$
• C. $(1,2)$
• D. $noneofthese$

Answer 1

The correct option is A $(1,1)$

Let the equation of the line is $ax+by+c=0$ ...(1)
Therefore
$\frac{2a+c}{\sqrt{a^2+b^2}}+\frac{2b+c}{\sqrt{a^2+b^2}}+\frac{a+b+c}{\sqrt{a^2+b^2}}=0$
or $a+b+c=0$ ...(2)
From (1) and (2)
$a(x-1)+b(y-1)=0$
which passes through the point $(1,1)$ for all values of $a,b.$