What is the shortest distance between two parallel lines in R^2: 3x + 4y - 5 = 0 and 3x + 4y + 15 = 0?
Answer and explanation
Correct answer: D. 4 units
- Step 1: Distance between parallel lines Ax + By + C1 = 0 and Ax + By + C2 = 0 is d = |C1 - C2| / sqrt(A^2 + B^2). Step 2. d = |-5 - 15| / sqrt(9 + 16) = |-20| / sqrt(25) = 20 / 5 = 4 units. Answer: 4 units. Why not the others: Normal vector magnitude is sqrt(3^2 + 4^2) = 5.
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