# L is 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 throughA. (1, 1)B. (2, 1)C. (1, 2)D. none of these

Let ax + by + c = 0 be the variable line. It is given that the algebraic sum of the distances
of the points (1, 1), (2, 0) and (0, 2) from the line is equal to zero.

3a + 3b + 3c = 0

a + b + c = 0

Substituting c = – a – b in ax + by + c = 0, we get:

ax + by – a – b = 0

a(x – 1) + b(y – 1) = 0

This line is of the form L1 + λL2 = 0, which passes through the intersection of L1 = 0 and L2 = 0, i.e. x – 1 = 0 and y – 1 = 0.

x = 1, y = 1

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