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Question
Find the perpendicular distance from the origin of the perpendicular from the point (1, 2) upon the straight line \[x - \sqrt{3}y + 4 = 0 .\]
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Solution
The equation of the line perpendicular to \[x - \sqrt{3}y + 4 = 0\] is \[\sqrt{3}x + y + \lambda = 0\].
This line passes through (1, 2).
\[\therefore \sqrt{3} + 2 + \lambda = 0\]
\[ \Rightarrow \lambda = - \sqrt{3} - 2\]
Substituting the value of \[\lambda\],we get
\[\sqrt{3}x + y - \sqrt{3} - 2 = 0\]
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