Question

Distance between two lines \(3x + 4y - 9 = 0\) and \(3x + 4y + 10 = 0\) is

• A. None of these
• B. 9/5 unit
• C. 10 units
• D. 19/5 unit

Hint:

For distance between two parallel lines, remember the formula involving the coefficients of the lines and their constants.

Answer 1

The Correct Option is B

The formula to calculate the distance between two parallel lines \(Ax + By + C_1 = 0\) and \(Ax + By + C_2 = 0\) is: \[ \text{Distance} = \frac{|C_2 - C_1|}{\sqrt{A^2 + B^2}} \] Substituting the values for the given lines \(3x + 4y - 9 = 0\) and \(3x + 4y + 10 = 0\): \[ \text{Distance} = \frac{|10 - (-9)|}{\sqrt{3^2 + 4^2}} = \frac{19}{5} \] Thus, the correct answer is \(19/5\) unit.