Part of CG-01 — Straight Lines

Distance Between Parallel Lines

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For parallel lines ax + by + c1 = 0 and ax + by + c2 = 0 (same coefficients of x and y), the distance is |c1 - c2| / sqrt(a2a^2 + b2b^2). Important: the coefficients of x and y must be identical (not just proportional) before applying this formula. If given 2x + 3y = 5 and 4x + 6y = 7, first rewrite the second as 2x + 3y = 3.5, then d = |5 - 3.5| / sqrt(4 + 9) = 1.5/sqrt(13).

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