1. What Is Perpendicular Slope?

The perpendicular slope is the negative reciprocal of the original line's slope. Two lines are perpendicular if their slopes satisfy this relationship and they intersect at right angles (90 degrees).

2. How Does the Calculator Work?

The calculator uses the perpendicular slope formula:

Where:

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

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

3. Importance of Perpendicular Slope

Details: Perpendicular slopes are fundamental in geometry for constructing right angles, finding equations of perpendicular lines, and solving many geometric problems.

4. Using the Calculator

Tips: Enter any non-zero slope value. The calculator will return the negative reciprocal. Vertical lines (undefined slope) and horizontal lines (zero slope) are special cases.

5. Frequently Asked Questions (FAQ)

Q1: What's the perpendicular slope of a horizontal line?
A: A horizontal line (slope 0) has a vertical perpendicular line (undefined slope).

Q2: What's the perpendicular slope of a vertical line?
A: A vertical line (undefined slope) has a horizontal perpendicular line (slope 0).

Q3: How do I find the equation of a perpendicular line?
A: Use the perpendicular slope and a point on the new line in the point-slope form: \( y - y_1 = m_{\text{perp}}(x - x_1) \).

Q4: Do parallel lines have related slopes?
A: Yes, parallel lines have identical slopes.

Q5: Can I use this for 3D lines?
A: No, this calculator is for 2D lines only. Perpendicularity in 3D involves dot products of direction vectors.