Single correct option
What is the distance between the parallel lines 6x + 8y = 24 and 3x + 4y − 2 = 0?
- A. 1.2
- B. 1.6
- C. 2.0
- D. 2.4
Show answer and solution
Answer: (C) 2.0
Make the coefficients identical first: 3x + 4y − 2 = 0 ⇔ 6x + 8y − 4 = 0. The other line is 6x + 8y − 24 = 0.
Distance = |c₁ − c₂| / √(a² + b²) = |−24 − (−4)| / √(36+64) = 20/10 = 2.0.
Check: the lines lie on the same side of the origin, at distances 24/10 = 2.4 and 4/10 = 0.4 from it, and 2.4 − 0.4 = 2.0.
Trap: forgetting to scale the second equation so a, b match before subtracting the constants.
Distance = |c₁ − c₂| / √(a² + b²) = |−24 − (−4)| / √(36+64) = 20/10 = 2.0.
Check: the lines lie on the same side of the origin, at distances 24/10 = 2.4 and 4/10 = 0.4 from it, and 2.4 − 0.4 = 2.0.
Trap: forgetting to scale the second equation so a, b match before subtracting the constants.
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