1. What is the Distance Formula?

The distance formula calculates the straight-line distance between two points in a 2D plane. It's derived from the Pythagorean theorem and is fundamental in geometry and various practical applications.

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.

3. Applications of Distance Calculation

Details: The distance formula is used in navigation, computer graphics, physics, engineering, and machine learning for measuring spatial relationships between points.

4. Using the Calculator

Tips: Enter coordinates for both points. The calculator accepts decimal values. The result is given in the same units as the input coordinates.

5. Frequently Asked Questions (FAQ)

Q1: Can this be used for 3D coordinates?
A: No, this calculator is for 2D only. The 3D distance formula includes a z-component: √((x₂-x₁)² + (y₂-y₁)² + (z₂-z₁)²).

Q2: Does the order of points matter?
A: No, distance is commutative - the result is the same regardless of which point you consider first.

Q3: What if I get a negative distance?
A: Distance is always positive. If you get a negative result, check your input values.

Q4: Can I use this for geographic coordinates?
A: For small distances on Earth's surface, this works as an approximation. For large distances, use the Haversine formula.

Q5: How precise is the calculation?
A: The calculator shows results rounded to 2 decimal places, but performs calculations with higher precision internally.