If the algebraic sum of the perpendiculars drawn from the points $(2, 0), (0, 2), (1, 1)$ to a variable line is zero, then the line will always pass through a fixed point whose co-ordinates are

(1, 1)

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(2, 2)

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(3, 3)

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(0, 0)

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Solution

The correct option is A $(1, 1)$
Let the variable line be
$a x + b y = 1 . . . (1)$
If it is given that the algebraic sum of perpendiculars drawn from the points $(2, 0), (0, 2), (1, 1)$ is zero.
$∴ \frac{2 a - 1}{\sqrt{a^{2} + b^{2}}} + \frac{2 b - 1}{\sqrt{a^{2} + b^{2}}} + \frac{a + b - 1}{\sqrt{a^{2} + b^{2}}} = 0$
$\Rightarrow 3 a + 3 b - 3 = 0$
$\Rightarrow a + b = 1 . . . (2)$
Comparing $(1)$ and $(2),$ we get
$(x, y) = (1, 1)$
So, variable line always passes through fixed point $(1, 1)$

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If the algebraic sum of the perpendiculars drawn from the points (2,0),(0,2),(1,1) to a variable line is zero, then the line will always pass through a fixed point whose co-ordinates are

If the algebraic sum of the perpendiculars drawn from the points $(2, 0), (0, 2), (1, 1)$ to a variable line is zero, then the line will always pass through a fixed point whose co-ordinates are