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:

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

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, computer graphics, physics (calculating displacement), machine learning (similarity measures), and many other fields that require spatial calculations.

4. Using the Calculator

Tips: Enter the coordinates of two points in 2D space. The calculator will compute the straight-line distance between them. Works with any real number coordinates.

5. Frequently Asked Questions (FAQ)

Q1: Does the order of points matter in the formula?
A: No, the distance is the same regardless of which point you consider first because the differences are squared.

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 if my points have the same x or y coordinate?
A: The formula simplifies. If x-coordinates are equal, it's just the absolute difference in y-coordinates, and vice versa.

Q4: How precise are the calculations?
A: The calculator provides results rounded to 2 decimal places, but uses full precision for intermediate calculations.

Q5: Can I use negative coordinates?
A: Yes, the formula works with any real numbers, including negative values.