1. What Is The Perpendicular Line Equation?

The perpendicular line equation calculates a line that intersects another line at a 90-degree angle. The slope of the perpendicular line is the negative reciprocal of the original line's slope.

2. How Does The Calculator Work?

The calculator uses the perpendicular line equation:

Where:

• \( y \) — Y-coordinate of any point on the perpendicular line
• \( y_1 \) — Known y-coordinate on the perpendicular line
• \( x \) — X-coordinate of any point on the perpendicular line
• \( x_1 \) — Known x-coordinate on the perpendicular line
• \( m \) — Slope of the original line
• \( -\frac{1}{m} \) — Slope of the perpendicular line (negative reciprocal)

Explanation: The perpendicular slope is calculated as the negative reciprocal of the original slope, then applied using the point-slope formula.

3. Importance Of Perpendicular Lines

Details: Perpendicular lines are fundamental in geometry, used in construction, engineering, computer graphics, and coordinate geometry. They help create right angles and orthogonal coordinate systems.

4. Using The Calculator

Tips: Enter the known point coordinates (x₁, y₁) and the original line's slope. The slope cannot be zero. The calculator provides both point-slope and slope-intercept forms of the perpendicular line equation.

5. Frequently Asked Questions (FAQ)

Q1: What if the original slope is zero?
A: If the original slope is zero (horizontal line), the perpendicular line will have an undefined slope (vertical line), and the equation becomes x = constant.

Q2: What if the original slope is undefined?
A: If the original slope is undefined (vertical line), the perpendicular line will have a slope of zero (horizontal line), and the equation becomes y = constant.

Q3: How do I verify lines are perpendicular?
A: Multiply the slopes of both lines. If the product equals -1, the lines are perpendicular.

Q4: Can I use this for 3D geometry?
A: This calculator is for 2D coordinate geometry. In 3D, perpendicularity involves dot products and is more complex.

Q5: What are practical applications?
A: Used in construction for right angles, computer graphics for orthogonal projections, navigation for perpendicular routes, and engineering for structural designs.