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  • If the algebraic sum of the perpendicular distances of a variable line from the points <img alt="(0,2)$, $(2,0)$ and $(1,1)" src="https://entrancecorner.oncodecogs.com/gif.latex?%280%2C2%29%24%2C%2

If the algebraic sum of the perpendicular distances of a variable line from the points (0,2)$, $(2,0)$ and $(1,1) is zero, then the line always passes through the point

Option: 1

(0,0)


Option: 2

(0,1)


Option: 3

(1,0)


Option: 4

(1,1)


Answers (1)

best_answer

If the line be \mathrm{a x+b y+c=0}, then \mathrm{\frac{0+2 b+c}{\sqrt{a^{2}+b^{2}}}+\frac{2 a+c}{\sqrt{a^{2}+b^{2}}}+\frac{a+b+c}{\sqrt{a^{2}+b^{2}}}=0}

\mathrm{\Rightarrow 3 a+3 b+3 c=0 \quad \Rightarrow a+b+c=0}

\mathrm{\Rightarrow} the line \mathrm{a x+b y+c=0} always passes through the point \mathrm{(1,1)}.

\mathrm{\therefore (d)}

Posted by

Pankaj Sanodiya

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