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What is the perpendicular distance of a point (2, 3) from the line 2x -…

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})

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