1. What is a Perpendicular Slope?

A perpendicular slope is the negative reciprocal of the original 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
• \( m_{\text{perp}} \) — Perpendicular slope

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

3. Importance of Perpendicular Slopes

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

4. Using the Calculator

Tips: Enter any non-zero slope value. The calculator will return the slope that would create a perpendicular line. Vertical lines (undefined slope) and horizontal lines (zero slope) are special cases.

5. Frequently Asked Questions (FAQ)

Q1: What if I enter a slope of zero?
A: A zero slope indicates a horizontal line. Its perpendicular would be a vertical line (undefined slope), which the calculator cannot display numerically.

Q2: What about vertical lines?
A: Vertical lines have undefined slope. Their perpendiculars are horizontal lines with zero slope.

Q3: Does this work for 3D planes?
A: No, this calculator is for 2D lines. Perpendicularity in 3D involves normal vectors.

Q4: How precise are the results?
A: Results are rounded to 4 decimal places. For exact fractions, consider manual calculation.

Q5: Can I use this for parallel lines?
A: No, parallel lines have identical slopes. This calculator is specifically for perpendicular slopes.