The algebraic sum of the perpendicular distances from the points (2,0), (0, 2) and (1, 1) to a variable straight line is zero. The line passes through a fixed point whose co-ordinates are
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Let the line by lx + my + 1 = 0. . . . (1)
According to the given condition
⇒ ⇒ l + m + 1 = 0 ⇒ ⇒ l(1) + m(1) + 1 = 0.
Comparing it with (1), we find that line (1) is passing through (1, 1).
Hence is the correct answer.
Alternate:
The three given points are collinear and (1, 1) is the mid-point of (2, 0) and (0, 2). Hence all the lines with given property will pass through (1, 1)
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