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.

2. How Does the Calculator Work?

The calculator uses the perpendicular slope formula:

Where:

• \( m \) — Original slope
• \( m_{\perp} \) — Perpendicular slope

Explanation: The negative reciprocal relationship ensures the lines intersect at 90 degrees.

3. Importance of Perpendicular Slopes

Details: Perpendicular slopes are essential in geometry, engineering, and physics for creating right angles and orthogonal relationships.

4. Using the Calculator

Tips: Enter any non-zero slope value. The calculator will return the perpendicular slope. Vertical lines (undefined slope) have horizontal perpendiculars (slope = 0) and vice versa.

5. Frequently Asked Questions (FAQ)

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

Q2: What if my original slope is undefined?
A: An undefined slope (vertical line) has a perpendicular slope of zero (horizontal line).

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

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

Q5: What about nearly parallel lines?
A: Lines with slopes that are nearly negative reciprocals will intersect at nearly 90 degrees.