1. What Is the Slope of a Perpendicular Line?

The slope of a line perpendicular to another is the negative reciprocal of the original line's slope. If two lines are perpendicular, the product of their slopes equals -1.

2. How Does the Calculator Work?

The calculator uses the perpendicular slope formula:

Where:

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

Explanation: This formula finds the slope of a line that forms a 90-degree angle with the original line. The negative reciprocal ensures the product of the slopes equals -1.

3. Importance of Perpendicular Slope Calculation

Details: Calculating perpendicular slopes is essential in geometry, engineering, and physics for constructing right angles, designing orthogonal components, and solving problems involving perpendicular relationships.

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 value.

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 undefined slope, which cannot be calculated with this formula.

Q2: What if the original slope is undefined?
A: An undefined slope represents a vertical line. Its perpendicular would be a horizontal line with slope 0.

Q3: Can this be used for 3D geometry?
A: No, this formula applies only to 2D coordinate geometry. In 3D, perpendicularity involves more complex vector calculations.

Q4: How are perpendicular slopes related in coordinate geometry?
A: Two lines are perpendicular if and only if the product of their slopes equals -1 (for non-vertical/non-horizontal lines).

Q5: What's the perpendicular slope if m = 2/3?
A: The perpendicular slope would be -3/2, which is the negative reciprocal of 2/3.