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 applied 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: Distance calculations are used in navigation, computer graphics, physics, engineering, and machine learning for measuring spatial relationships between objects.

4. Using the Calculator

Tips: Enter the coordinates of two points in the 2D plane. The calculator will compute the Euclidean distance between them. Coordinates can be positive, negative, or decimal values.

5. Frequently Asked Questions (FAQ)

Q1: Does the order of points matter in the calculation?
A: No, the distance is the same whether you calculate from point A to B or point B to A.

Q2: Can this be extended to 3D space?
A: Yes, for 3D points (x₁,y₁,z₁) and (x₂,y₂,z₂), the formula becomes √[(x₂-x₁)² + (y₂-y₁)² + (z₂-z₁)²].

Q3: What units does the distance use?
A: The distance is in the same units as the input coordinates. If coordinates are in meters, distance will be in meters.

Q4: How accurate is the calculation?
A: The calculator provides results with 4 decimal places, but accuracy depends on the precision of your input coordinates.

Q5: What's the difference between Euclidean and Manhattan distance?
A: Euclidean distance is straight-line distance, while Manhattan distance is the sum of absolute differences (like moving along city blocks).