Given:
Line x - √3y + 4 = 0
To find:
The perpendicular distance from the origin of the perpendicular from the point (1, 2) upon the straight line x - √3y + 4 = 0 .
Concept Used:
Distance of a point from a line.
Explanation:
The equation of the line perpendicular to x - √3y + 4 = 0 is x - √3y + λ = 0 This line passes through (1,2)
∴ \(\sqrt{-3}\) + 2 + λ = 0
⇒ λ = \(\sqrt{-3}\) - 2
Substituting the value of λ, we get \(\sqrt{3}x+y-\sqrt{3}-2=0\)
Let d be the perpendicular distance from the origin to the line \(\sqrt{3}x+y-\sqrt{3}-2=0\)
d = \(\frac{0-0-\sqrt{3}-2}{\sqrt{1+3}}=\frac{\sqrt{3}+2}{2}\)
Hence, the required perpendicular distance is \(\frac{\sqrt{3}+2}{2}\)
