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CAT 2023 Slot 1 · Quant · Coordinate Geometry · medium

Find the perpendicular distance from the point (3, 4) to the line 3x − 4y + 10 = 0.

Single correct option

Find the perpendicular distance from the point (3, 4) to the line 3x − 4y + 10 = 0.
  1. A. 0.4
  2. B. 0.6
  3. C. 0.8
  4. D. 1.0
Show answer and solution

Answer: (B) 0.6

Distance from (x₀,y₀) to line ax+by+c=0 is |ax₀+by₀+c|/√(a²+b²). Here a=3, b=−4, c=10, (x₀,y₀)=(3,4). Numerator = |3×3 − 4×4 + 10| = |9−16+10| = |3| = 3. Denominator = √(9+16) = 5. Distance = 3/5 = 0.6.
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Original question written in the CAT 2023 Slot 1 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake