1. What is the Distance Formula?

The distance formula calculates the straight-line distance between two points in a 2D coordinate system. It is derived from the Pythagorean theorem and is fundamental in geometry, physics, and engineering applications.

2. How Does the Calculator Work?

The calculator uses the distance formula:

Where:

• \( D \) — Distance between the two 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 between the two points.

3. Applications of Distance Calculation

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

4. Using the Calculator

Tips: Enter the coordinates of both points. The calculator accepts any real numbers for coordinates and will compute the Euclidean distance between them.

5. Frequently Asked Questions (FAQ)

Q1: Can this calculator handle 3D coordinates?
A: No, this calculator is designed for 2D coordinates only. For 3D distance calculation, the formula extends to include the z-coordinate: \( D = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2} \)

Q2: What units does the distance result use?
A: The distance is in the same units as the input coordinates. If coordinates are in meters, the distance will be in meters.

Q3: Can I use negative coordinates?
A: Yes, the calculator works with both positive and negative coordinate values.

Q4: How accurate is the calculation?
A: The calculation uses double-precision floating-point arithmetic, providing high accuracy for most practical applications.

Q5: Does the order of points matter?
A: No, the distance between point A and point B is the same as between point B and point A due to the squaring of differences.