1. What is the Opposite Reciprocal?

The opposite reciprocal of a slope is the negative inverse of the original slope. It represents the slope of a line that is perpendicular to the original line.

2. How Does the Calculator Work?

The calculator uses the opposite reciprocal formula:

Where:

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

Explanation: To find a perpendicular slope, take the reciprocal of the original slope and change its sign.

3. Importance of Perpendicular Slopes

Details: Perpendicular slopes are essential in geometry for constructing right angles, determining orthogonal vectors, and solving problems involving perpendicular bisectors.

4. Using the Calculator

Tips: Enter any non-zero slope value. The calculator will return the slope of a line that would be perpendicular to a line with the given slope.

5. Frequently Asked Questions (FAQ)

Q1: What if my original slope is zero?
A: A horizontal line (slope 0) has a vertical line as its perpendicular (undefined slope). The calculator will show an error for zero input.

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

Q3: How is this used in real-world applications?
A: Used in construction (right angles), computer graphics (normal vectors), and physics (orthogonal components).

Q4: Does this work for 3D planes?
A: The concept extends to 3D, but the calculation becomes more complex involving cross products.

Q5: What's the relationship between the slopes of perpendicular lines?
A: Their product is -1 (m₁ × m₂ = -1).