1. What is a Perpendicular Slope?

A perpendicular slope is the negative reciprocal of the original line's slope. Two lines are perpendicular if the product of their slopes is -1 (except for vertical and horizontal lines).

2. How Does the Calculator Work?

The calculator uses the perpendicular slope formula:

Where:

• \( m \) — Original slope of the line
• \( m_{\text{perp}} \) — Slope of the perpendicular line

Special Cases:

• If original slope is 0 (horizontal line), perpendicular slope is undefined (vertical line)
• If original slope is undefined (vertical line), perpendicular slope is 0 (horizontal line)

3. Importance of Perpendicular Slopes

Applications: Perpendicular slopes are essential in geometry for constructing right angles, in architecture for designing orthogonal structures, and in coordinate geometry problems.

4. Using the Calculator

Instructions: Enter the slope of your original line. The calculator will compute the slope of a line that would be perpendicular to it. Any real number is valid except zero (use very small numbers like 0.0001 for near-vertical lines).

5. Frequently Asked Questions (FAQ)

Q1: What if my original slope is zero?
A: A horizontal line (slope 0) has a perpendicular line that's vertical (undefined slope).

Q2: What if my original slope is undefined?
A: A vertical line (undefined slope) has a perpendicular line that's horizontal (slope 0).

Q3: How do I verify two lines are perpendicular?
A: Multiply their slopes - if the product is -1, they're perpendicular.

Q4: Does this work for 3D lines?
A: No, this calculator is for 2D lines only. Perpendicularity in 3D requires vector analysis.

Q5: Can I use fractions as input?
A: Yes, the calculator accepts decimal numbers which can represent fractions.