1. What is the Distance Formula?

The distance formula calculates the straight-line distance between two points in a 2D plane. It is derived from the Pythagorean theorem and is fundamental in geometry and various applied mathematics fields.

2. How Does the Calculator Work?

The calculator uses the distance formula:

Where:

• \( (x_1, y_1) \) — Coordinates of the first point
• \( (x_2, y_2) \) — Coordinates of the second point

Explanation: The formula calculates the hypotenuse of a right triangle formed by the differences in x and y coordinates between the two points.

3. Applications of Distance Calculation

Details: The distance formula is used in geometry, physics, computer graphics, navigation systems, and many engineering applications where measuring spatial relationships is important.

4. Using the Calculator

Tips: Enter the x and y coordinates for both points. The calculator works with any real numbers (positive or negative) and will return the distance in the same units as your input coordinates.

5. Frequently Asked Questions (FAQ)

Q1: Does the order of points matter in the calculation?
A: No, the distance is the same regardless of which point you consider first because the differences are squared.

Q2: Can this be used for 3D coordinates?
A: This calculator is for 2D only. For 3D, you would add a z-coordinate term: √[(x₂-x₁)² + (y₂-y₁)² + (z₂-z₁)²].

Q3: What if my points have the same x or y coordinate?
A: The formula still works. If x-coordinates are equal, you're calculating vertical distance. If y-coordinates are equal, it's horizontal distance.

Q4: How precise is the calculation?
A: The calculator shows results rounded to 2 decimal places, but uses full precision in calculations.

Q5: Can I use this for geographical coordinates?
A: For small distances on Earth, this works as an approximation. For large distances, you would need the haversine formula that accounts for Earth's curvature.