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
jamb 1992mathematics

The correct answer is A. \(\frac{\sqrt{5}}{2}\)

2x - 4y + 3 = 0

Required distance = \(\frac{(2 \times 2) + 3(-4) + 3}{\sqrt{2^2} + (-4)^2}\)

= \(\frac{4 - 12 + 3}{\sqrt{20}}\)

= \(\frac{-5}{-2\sqrt{5}}\)

= \(\frac{\sqrt{5}}{2}\)

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