1. What is the Perpendicular Slope?

The perpendicular slope is the slope of a line that forms a 90-degree angle with another line. In coordinate geometry, two lines are perpendicular if and only if the product of their slopes equals -1.

2. How Does the Calculator Work?

The calculator uses the perpendicular slope formula:

Where:

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

Explanation: The negative reciprocal relationship ensures that the two lines intersect at right angles (90 degrees).

3. Importance of Perpendicular Slopes

Details: Perpendicular slopes are fundamental in geometry, architecture, engineering, and computer graphics for creating right angles and orthogonal relationships between lines and surfaces.

4. Using the Calculator

Tips: Enter the original slope value. The slope cannot be zero (division by zero error). The result will be the negative reciprocal of the input slope.

5. Frequently Asked Questions (FAQ)

Q1: What happens if the original slope is zero?
A: The perpendicular slope would be undefined (division by zero), representing a vertical line.

Q2: What if the original slope is undefined (vertical line)?
A: The perpendicular slope would be zero, representing a horizontal line.

Q3: How do perpendicular slopes relate to right angles?
A: Two lines are perpendicular if and only if the product of their slopes equals -1, ensuring a 90-degree intersection.

Q4: Can this formula be used in 3D space?
A: In 3D geometry, the concept extends to perpendicular vectors, but the simple slope formula applies only to 2D coordinate systems.

Q5: What are practical applications of perpendicular slopes?
A: Used in construction for right angles, computer graphics for orthogonal projections, and navigation for perpendicular routes.