Question

Let the algebric sum of the perpendicular distances from the points (2, 0), (0, 2), (1, 1) to a variable straight line be zero, then the line passes through a fixed point whose co-ordinates are
(I.I.T 1991)

• A. (1, 1)
• B. (2, 2)
• C. (0, 0)
• D. none

Answer 1

The correct option is A

(1, 1)

Let the variable line be px + qy +1 = 0, then given condition
$p_1+p_2+p_3\Rightarrow$ 3p + 3q + 3 = 0 or p + q + 1 = 0
Condition (1) shows that the variable line passes through the point (1, 1).