Numerical answer
What is the distance between the parallel lines 3x + 4y = 12 and 6x + 8y + 11 = 0?
Show answer and solution
Answer: 3.5
First make the coefficients of x and y match. Divide the second equation by 2: 3x + 4y + 5.5 = 0. The first is 3x + 4y − 12 = 0.
Distance = |c₁ − c₂| / √(a² + b²) = |−12 − 5.5| / √(9 + 16) = 17.5/5 = 3.5.
Common error: using 11 instead of 5.5 without rescaling gives the wrong answer 4.6. The coefficients must be identical before applying the formula.
Distance = |c₁ − c₂| / √(a² + b²) = |−12 − 5.5| / √(9 + 16) = 17.5/5 = 3.5.
Common error: using 11 instead of 5.5 without rescaling gives the wrong answer 4.6. The coefficients must be identical before applying the formula.
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