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, physics, and many applied sciences.

2. How Does the Calculator Work?

The calculator uses the distance formula:

Where:

• \( d \) — Distance between the 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.

3. Applications of Distance Calculation

Details: Used in navigation, computer graphics, physics, engineering, and anywhere spatial relationships between points need to be measured.

4. Using the Calculator

Tips: Enter coordinates for both points. The calculator works with any real numbers (positive or negative). Results are in the same units as the input coordinates.

5. Frequently Asked Questions (FAQ)

Q1: Does the formula work in 3D space?
A: The 2D formula can be extended to 3D by adding a z-term: \( d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2 + (z_2-z_1)^2} \)

Q2: What if my points have the same x or y coordinate?
A: The formula still works. If x-coordinates are equal, distance equals the absolute difference in y-coordinates, and vice versa.

Q3: Can I use this for geographical coordinates?
A: For small distances on Earth, this works as approximation. For large distances, use the haversine formula that accounts for Earth's curvature.

Q4: Does the order of points matter?
A: No, distance is the same whether you calculate from point A to B or B to A.

Q5: How precise are the results?
A: Results are rounded to 4 decimal places. For higher precision, use more decimal places in input values.