What is the perpendicular distance of a point (2, 3) from the line 2x – 4y + 3 = 0?
-
A.
(frac{sqrt{5}}{2}) -
B.
(frac{sqrt{5}}{20}) -
C.
(frac{5}{sqrt{13}}) -
D.
6
Correct Answer: Option A
Explanation
2x – 4y + 3 = 0
Required distance = (frac{(2 times 2) + 3(-4) + 3}{sqrt{2^2} + (-4)^2})
= (frac{4 – 12 + 3}{sqrt{20}})
= (frac{-5}{-2sqrt{5}})
= (frac{sqrt{5}}{2})