1. What Is The Perpendicular Line Equation?

The perpendicular line equation calculates a line that intersects another line at a 90-degree angle. Given a line with slope m, the perpendicular line will have a slope of -1/m.

2. How Does The Calculator Work?

The calculator uses the perpendicular line formula:

Where:

• \( m_{\perp} \) — Perpendicular slope (unitless)
• \( m \) — Original slope (unitless)
• \( x \) — X coordinate (unitless)
• \( y \) — Y coordinate (unitless)
• \( b \) — Y-intercept (unitless)

Explanation: The calculator finds the equation of a line perpendicular to the original line that passes through a given point (x, y).

3. Importance Of Perpendicular Lines

Details: Perpendicular lines are fundamental in geometry, engineering, and computer graphics. They're used in constructing right angles, calculating distances, and solving geometric problems.

4. Using The Calculator

Tips: Enter the original slope and a point (x,y) that the perpendicular line should pass through. The original slope cannot be zero.

5. Frequently Asked Questions (FAQ)

Q1: What if the original slope is zero?
A: A horizontal line (slope 0) has a perpendicular line that is vertical (undefined slope), which cannot be represented in slope-intercept form.

Q2: Can I use this for vertical lines?
A: Vertical lines have undefined slope, so this calculator cannot process them as the original line.

Q3: What's the relationship between perpendicular slopes?
A: The slopes of perpendicular lines are negative reciprocals of each other (m₁ × m₂ = -1).

Q4: Does this work in 3D space?
A: No, this calculator is designed for 2D coordinate geometry only.

Q5: How precise are the results?
A: Results are calculated with high precision but displayed rounded to 4 decimal places for readability.