Formula Overview

Parallel lines share the same coefficients for x and y. For lines ax + by + c₁ = 0 and ax + by + c₂ = 0, the perpendicular distance d is:

d = \frac{|c₂ – c₁|}{\sqrt{a² + b²}}

Rewrite the given equations in standard form: 2x + 5y – 7 = 0 and 2x + 5y – 15 = 0. Here, a = 2, b = 5, c₁ = -7, c₂ = -15.

Step-by-Step Calculation

1. Substitute values: |c₂ – c₁| = |-15 – (-7)| = |-8| = 8
2. Denominator: \sqrt{2² + 5²} = \sqrt{4 + 25} = \sqrt{29} ≈ 5.385
3. Thus, d = \frac{8}{\sqrt{29}} ≈ \frac{8}{5.385} ≈ 1.48597
4. Rounded to two decimals: 1.49

Common Options Explained

In multiple-choice contexts, options might include:

• 1.48: Under-rounded value before precise check
• 1.49: Correct rounded answer (1.48597 ≈ 1.49)
• 1.50: Over-approximation ignoring exact sqrt
• 8/√29: Unrounded exact form, not decimal

The correct choice is 1.49, as it matches standard rounding (1.48597 to two decimals).