1. What is a Perpendicular Slope?

A perpendicular slope is the negative reciprocal of the original slope. If two lines are perpendicular, the product of their slopes equals -1. This relationship is fundamental in coordinate geometry and linear algebra.

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 a 90-degree angle, forming right angles where they meet.

3. Importance of Perpendicular Slopes

Details: Perpendicular slopes are essential in geometry, engineering, architecture, and computer graphics for creating right angles, orthogonal designs, and perpendicular bisectors.

4. Using the Calculator

Tips: Enter the original slope value. The slope cannot be zero (as division by zero is undefined). The result will be the perpendicular slope.

5. Frequently Asked Questions (FAQ)

Q1: What happens if the original slope is zero?
A: A slope of zero represents a horizontal line. Its perpendicular would be a vertical line with an undefined slope, which cannot be calculated with this formula.

Q2: What if the original slope is undefined (vertical line)?
A: The perpendicular to a vertical line is a horizontal line with a slope of zero.

Q3: Can this formula be used in 3D space?
A: In 3D geometry, the concept extends to normal vectors, but the simple reciprocal relationship applies specifically to 2D coordinate systems.

Q4: How are perpendicular slopes used in real-world applications?
A: They're used in construction for right angles, in computer graphics for orthogonal projections, and in navigation for calculating perpendicular courses.

Q5: What's the relationship between perpendicular slopes and negative reciprocals?
A: They are equivalent concepts. The negative reciprocal of any non-zero number will always give the slope of a line perpendicular to the original.