Perpendicular distance from a point to a line — A/L Combined Mathematics

How do I practise Perpendicular distance from a point to a line?

1 question with a worked solution

1. What is the perpendicular distance from the point (1, -2) to the straight line 3x - 4y + 9 = 0?
   1. A) 5 units
   2. B) 2 units
   3. C) 4 units
   4. D) 3 units
   Check my answer

   Correct answer: C) 4 units

   Using the perpendicular distance formula d = |a x₀ + b y₀ + c| / √(a² + b²): d = |3(1) - 4(-2) + 9| / √(3² + (-4)²) = |3 + 8 + 9| / √(9 + 16) = |20| / √25 = 20 / 5 = 4 units.

   Show worked solution

   Step 1: Formula: d = |a x₀ + b y₀ + c| / √(a² + b²). Step 2: Numerator: |3(1) - 4(-2) + 9| = |3 + 8 + 9| = 20. Step 3: Denominator: √(3² + 4²) = 5. Step 4: d = 20 / 5 = 4 units. Answer: 4 units.
   Modelled on: the A/L Combined Mathematics examination pattern

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Where does Perpendicular distance from a point to a line fit in the syllabus?

Year 1 · Term 3