1. What is a Perpendicular Line?

A perpendicular line is a straight line that makes a right angle (90 degrees) with another line. Given a line with slope m, the slope of a perpendicular line is the negative reciprocal (-1/m).

2. How Does the Calculator Work?

The calculator uses the perpendicular line equation:

Where:

• \( m \) — Slope of the original line
• \( (x_1, y_1) \) — Point through which the perpendicular line must pass
• \( -\frac{1}{m} \) — Slope of the perpendicular line

Explanation: The calculator first finds the negative reciprocal of the original slope, then uses the point-slope form to create the equation of the perpendicular line.

3. Importance of Perpendicular Lines

Details: Perpendicular lines are fundamental in geometry and have many practical applications in construction, engineering, and computer graphics where right angles are required.

4. Using the Calculator

Tips: Enter the slope of the original line and the coordinates of the point through which the perpendicular line should pass. The calculator will provide both slope-intercept and point-slope forms of the equation.

5. Frequently Asked Questions (FAQ)

Q1: What if the original line is horizontal?
A: The perpendicular line will be vertical with an undefined slope, represented by the equation x = constant.

Q2: What if the original line is vertical?
A: The perpendicular line will be horizontal with a slope of 0.

Q3: Can I use this for 3D lines?
A: No, this calculator is for 2D lines only. Perpendicularity in 3D requires vector calculations.

Q4: How precise are the results?
A: Results are rounded to 2 decimal places for clarity, but calculations use full precision.

Q5: What if I enter a slope of 0?
A: The calculator will handle this special case and return the equation of a vertical line.