Question

Let the algebraic sum of the perpendicular distance from the points (2,0), (0,2), and (1, 1) to a variable straight line be zero. Then the line passes through a fixed point whose coordinate are ___

• A. (0,0)
• B. (1,1)
• C. (2,2)
• D. (3,3)

Answer 1

The correct option is B (1,1)

Let the variable line be
$ax+by+c=0...\left(i\right)$
Then the perpendicular distance of the line from (2,0) is
$p_1=\frac{2a+c}{\sqrt{a^2+b^2}}$
The perpendicular distance of the line from (0,2) is
$p_2=\frac{2b+c}{\sqrt{a^2+b^2}}$
The perpendicaler distance of the line from (1,1) is
$p_3=\frac{a+b+c}{\sqrt{a^2+b^2}}$
According to question,
$p_1+p_2+p_3=0or\frac{2a+c+2b+c+a+b+c}{\sqrt{a^2+b^2}}=0or3a+3b+3c=0ora+b+c=0...\left(ii\right)$
Form (i) and (ii) we can say that variable line (i) passes through the fixed point (1,1).