1. What is the Point-Slope Form for Perpendicular Lines?

The point-slope form for a perpendicular line calculates the equation of a line that is perpendicular to a given line and passes through a specific point. The perpendicular slope is the negative reciprocal of the original slope.

2. How Does the Calculator Work?

The calculator uses the perpendicular line equation:

Where:

• \( y \) — Dependent variable (unitless)
• \( y₁ \) — Y-coordinate of the point (unitless)
• \( m_{\perp} \) — Perpendicular slope (unitless)
• \( x \) — Independent variable (unitless)
• \( x₁ \) — X-coordinate of the point (unitless)
• \( m \) — Original slope (unitless)

Explanation: The perpendicular slope is calculated as the negative reciprocal of the original slope, and the equation is constructed using the point-slope form.

3. Importance of Perpendicular Line Calculation

Details: Calculating perpendicular lines is essential in geometry, engineering, and computer graphics for creating right angles, constructing perpendicular bisectors, and solving various geometric problems.

4. Using the Calculator

Tips: Enter the coordinates of the point (x₁, y₁) and the original slope (m). The original slope cannot be zero. All values can be integers or decimals.

5. Frequently Asked Questions (FAQ)

Q1: Why can't the original slope be zero?
A: A slope of zero would result in division by zero when calculating the perpendicular slope, which is undefined.

Q2: What is the perpendicular slope of a vertical line?
A: A vertical line has undefined slope, so its perpendicular line would be horizontal with slope 0.

Q3: How do I verify if two lines are perpendicular?
A: Multiply their slopes. If the product is -1, the lines are perpendicular.

Q4: Can I use this for 3D geometry?
A: No, this calculator is for 2D geometry. Perpendicularity in 3D involves more complex vector calculations.

Q5: What if I have two points instead of a slope?
A: First calculate the slope using m = (y₂ - y₁)/(x₂ - x₁), then use that slope in this calculator.