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 engineering applications.

2. How Does the Calculator Work?

The calculator uses the distance formula:

Where:

• \( d \) — Distance between the points
• \( (x_1, y_1) \) — Coordinates of first point
• \( (x_2, y_2) \) — Coordinates of second point

Explanation: The formula calculates the hypotenuse of a right triangle formed by the differences in x and y coordinates.

3. Applications of the Distance Formula

Details: Used in navigation systems, computer graphics, physics (calculating displacements), machine learning (similarity measures), and many other fields requiring spatial analysis.

4. Using the Calculator

Tips: Enter coordinates for both points. The calculator accepts any real numbers (positive or negative). The result is always non-negative.

5. Frequently Asked Questions (FAQ)

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

Q2: Can this be extended to 3D space?
A: Yes, the 3D distance formula is \( d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2 + (z_2-z_1)^2} \).

Q3: What units does the calculator use?
A: The result is in the same units as the input coordinates (meters, feet, etc.).

Q4: How accurate is the calculation?
A: The calculator provides results with 4 decimal places of precision.

Q5: What if I get a distance of zero?
A: A zero distance means both points have identical coordinates.