1. What is Euclidean Distance?

Euclidean distance is the straight-line distance between two points in a 2D plane. It's derived from the Pythagorean theorem and represents the shortest path between two points in Euclidean space.

2. How Does the Calculator Work?

The calculator uses the Euclidean distance formula:

Where:

• \( d \) — Euclidean distance between points
• \( x_1, y_1 \) — 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, providing the straight-line distance.

3. Importance of Distance Calculation

Details: Euclidean distance is fundamental in mathematics, physics, computer graphics, machine learning, and navigation systems. It's used for proximity analysis, clustering algorithms, and spatial relationships.

4. Using the Calculator

Tips: Enter the x and y coordinates for both points. The calculator accepts any real numbers and provides the distance in the same units as the input coordinates.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between Euclidean and Manhattan distance?
A: Euclidean distance is straight-line distance, while Manhattan distance is the sum of absolute differences in coordinates (like moving along city blocks).

Q2: Can this calculator be used for 3D points?
A: No, this calculator is specifically for 2D points. For 3D points, the formula extends to \( d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2 + (z_2-z_1)^2} \).

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

Q4: Can I use negative coordinates?
A: Yes, the calculator handles negative coordinates as they represent positions in different quadrants of the coordinate plane.

Q5: How accurate is the calculation?
A: The calculator provides results with 4 decimal places precision, suitable for most applications requiring distance measurements.