What is the distance between the two parallel lines: 3x - 4y + 7 = 0 and 3x - 4y - 18 = 0?
Answer and explanation
Correct answer: A. 5 units
- Step 1: The distance d between two parallel lines Ax + By + C_1 = 0 and Ax + By + C_2 = 0 is given by: d = |C_1 - C_2| / sqrt(A^2 + B^2).
- Step 2: Here, A = 3, B = -4, C_1 = 7, and C_2 = -18.
- Step 3: Calculate numerator: |7 - (-18)| = |7 + 18| = 25.
- Step 4: Calculate denominator: sqrt(3^2 + (-4)^2) = sqrt(9 + 16) = sqrt(25) = 5.
- Step 5: d = 25 / 5 = 5 units.
Answer
5 units.
Why not the others: '25 units' forgets to divide by sqrt(A^2 + B^2); '2.2 units' subtracts 18 - 7 = 11 in numerator; '11 units' forgets the denominator and signs.
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