1. What is the Distance Formula?

The distance formula is derived from the Pythagorean theorem and calculates the straight-line distance between two points in a Cartesian coordinate system. It's a fundamental concept in geometry, physics, and many applied sciences.

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: Distance calculation is essential in various fields including navigation, computer graphics, physics, engineering, and geographic information systems (GIS).

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: Can this formula be used in 3D space?
A: No, this is the 2D distance formula. For 3D points, the formula extends to: √[(x₂-x₁)² + (y₂-y₁)² + (z₂-z₁)²]

Q2: Does the order of points matter?
A: No, the distance is the same regardless of which point is considered first because we're squaring the differences.

Q3: What if I have negative coordinates?
A: The formula works correctly with negative coordinates as the differences are squared, eliminating any negative signs.

Q4: How accurate is the calculation?
A: The calculator provides high precision with up to 4 decimal places, suitable for most applications.

Q5: Can I use this for geographical distances?
A: For small distances on Earth's surface, this provides a good approximation. For longer distances, you would need to account for Earth's curvature using the Haversine formula.