1. What Are Parallel and Perpendicular Lines?

Parallel lines are lines in a plane that never meet; they have the same slope but different y-intercepts. Perpendicular lines intersect at right angles (90 degrees); their slopes are negative reciprocals of each other.

2. How Does the Calculator Work?

The calculator uses the line equation:

Where:

• \( m \) — Slope of the line
• \( b \) — Y-intercept of the line

For parallel lines: The slope remains the same, and the new intercept is calculated using the given point.

For perpendicular lines: The slope becomes the negative reciprocal (-1/m), and the new intercept is calculated using the given point.

3. Importance in Geometry

Details: Understanding parallel and perpendicular lines is fundamental in geometry, architecture, engineering, and many practical applications like road design and construction.

4. Using the Calculator

Tips: Enter the slope (m) and y-intercept (b) of your original line, plus the coordinates of a point you want the new lines to pass through. The calculator will provide equations for both parallel and perpendicular lines through that point.

5. Frequently Asked Questions (FAQ)

Q1: What if my original line is horizontal?
A: A parallel line will also be horizontal. The perpendicular line will be vertical (undefined slope) with equation x = constant.

Q2: What if my original line is vertical?
A: A parallel line will also be vertical. The perpendicular line will be horizontal (slope = 0).

Q3: Can I use this for 3D lines?
A: No, this calculator is for 2D lines only. 3D lines require 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 get "undefined" for a slope?
A: This occurs with vertical lines, which have undefined slope. The equation will be in the form x = constant.