1. What is Distance Between Two Parallel Lines?

The distance between two parallel lines is the shortest perpendicular distance between them. For lines in slope-intercept form (y = mx + b), this distance can be calculated using a specific mathematical formula.

2. How Does the Calculator Work?

The calculator uses the distance formula for parallel lines:

Where:

• \( m \) — Slope of both parallel lines
• \( b_1 \) — Y-intercept of the first line
• \( b_2 \) — Y-intercept of the second line

Explanation: The formula calculates the perpendicular distance between two lines that have the same slope but different intercepts.

3. Importance of Distance Calculation

Details: Calculating distance between parallel lines is fundamental in geometry, engineering, computer graphics, and various scientific applications where spatial relationships are important.

4. Using the Calculator

Tips: Enter the slope (m) and the y-intercepts (b₁ and b₂) of both parallel lines. The calculator will compute the perpendicular distance between them.

5. Frequently Asked Questions (FAQ)

Q1: What if the lines are not parallel?
A: This formula only works for parallel lines. For non-parallel lines, they will intersect and the distance between them is zero at the intersection point.

Q2: Can this formula be used for vertical lines?
A: No, vertical lines have undefined slope. For vertical lines x = c₁ and x = c₂, the distance is simply |c₁ - c₂|.

Q3: What is the unit of the distance?
A: The distance unit depends on the coordinate system units. If coordinates are in meters, distance will be in meters.

Q4: How is this formula derived?
A: It's derived from the point-to-line distance formula, using the fact that parallel lines have the same slope.

Q5: Can this be used in 3D space?
A: No, this formula is for 2D coordinate geometry. For 3D parallel lines, a different approach is needed.