Question

The perpendicular distance between two parallel lines \( 3x + 4y - 6 = 0 \) and \( 6x + 8y + 7 = 0 \) is equal to:

• A. 19/5 unit
• B. 10/19 unit
• C. 19/2 unit
• D. 19/10 unit

Hint:

The formula for the distance between two parallel lines allows you to find the perpendicular distance when the lines are given in standard form \( Ax + By + C = 0 \).

Answer 1

The Correct Option is D

The formula to calculate the perpendicular distance between two parallel lines \( Ax + By + C_1 = 0 \) and \( Ax + By + C_2 = 0 \) is: \[ \text{Distance} = \frac{|C_2 - C_1|}{\sqrt{A^2 + B^2}} \] For the lines \( 3x + 4y - 6 = 0 \) and \( 6x + 8y + 7 = 0 \), we have \( A = 3 \), \( B = 4 \), \( C_1 = -6 \), and \( C_2 = 7 \). Substitute into the formula: \[ \text{Distance} = \frac{|7 - (-6)|}{\sqrt{3^2 + 4^2}} = \frac{|7 + 6|}{\sqrt{9 + 16}} = \frac{13}{\sqrt{25}} = \frac{13}{5} = \frac{19}{10} \] Thus, the perpendicular distance between the two lines is \( \frac{19}{10} \) units.