1. What Are Perpendicular Lines?

Perpendicular lines are two lines that intersect at a right angle (90 degrees). In coordinate geometry, the relationship between their slopes is defined by a specific mathematical formula.

2. How Does the Calculator Work?

The calculator uses the perpendicular lines formula:

Where:

• \( m_1 \) — Slope of the first line
• \( m_2 \) — Slope of the perpendicular line

Explanation: The slope of a perpendicular line is the negative reciprocal of the original line's slope. If the original slope is positive, the perpendicular slope is negative, and vice versa.

3. Importance of Perpendicular Lines

Details: Perpendicular lines are fundamental in geometry, architecture, engineering, and design. They ensure structural stability, create right angles in construction, and are essential in coordinate geometry problems.

4. Using the Calculator

Tips: Enter the slope of the first line. The slope cannot be zero (horizontal line) as its perpendicular would be undefined (vertical line). For best results, use exact fractions or decimal values.

5. Frequently Asked Questions (FAQ)

Q1: What happens if the original slope is zero?
A: If m₁ = 0 (horizontal line), the perpendicular line would be vertical with an undefined slope. The calculator requires non-zero input.

Q2: Can I use this for lines in 3D space?
A: No, this formula applies only to 2D coordinate geometry. In 3D, perpendicularity involves dot products and is more complex.

Q3: What if both slopes are the same?
A: If m₁ = m₂, the lines are parallel, not perpendicular. Perpendicular lines always have slopes that are negative reciprocals of each other.

Q4: How do I verify lines are perpendicular?
A: Multiply the slopes: if m₁ × m₂ = -1, the lines are perpendicular. This is the mathematical test for perpendicularity.

Q5: Can I use this for curved lines?
A: This formula applies only to straight lines. For curves, perpendicularity is determined by the slopes of tangent lines at the point of intersection.