Question

$L$ is a variable line such that the algebraic sum of the distances of the points $(1,1)$ and $(2,0)$ 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. $(2,2)$

Answer 1

Answer: (A)

$(1,1)$

Observe that the given points lie on a single line

The point $(1,1)$ is midpoint of $(2,0)$ and $(0,2)$

So the distance from point $(2,0)$ to $(1,1)$ is equal to the distance from point $(0,2)$ to $(1,1)$ but they lie on opposite sides of point $(1,1)$

Therefore the algebraic sum of distances will be zero

Therefore the line $L$ will always pass through the point $(1,1)$

So the correct option is $A$