Numerical answer
What is the distance between the parallel lines 3x + 4y = 12 and 6x + 8y + 6 = 0?
Show answer and solution
Answer: 3
First make the coefficients of x and y identical. 6x + 8y + 6 = 0 ⇔ 3x + 4y + 3 = 0.
The lines are 3x + 4y − 12 = 0 and 3x + 4y + 3 = 0.
Distance = |c₁ − c₂|/√(a² + b²) = |−12 − 3|/√(9 + 16) = 15/5 = 3 units.
The trap is to use the constants 12 and 6 directly without first scaling the second equation, which gives a wrong answer.
The lines are 3x + 4y − 12 = 0 and 3x + 4y + 3 = 0.
Distance = |c₁ − c₂|/√(a² + b²) = |−12 − 3|/√(9 + 16) = 15/5 = 3 units.
The trap is to use the constants 12 and 6 directly without first scaling the second equation, which gives a wrong answer.
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