1. What is the Distance Formula?

The distance formula calculates the straight-line distance between two points in a coordinate plane. It is derived from the Pythagorean theorem and is fundamental in geometry, physics, and various applications involving spatial relationships.

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

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

3. Importance of Distance Calculation

Details: Distance calculation is essential in mathematics, physics, engineering, computer graphics, navigation systems, and many real-world applications where measuring the shortest path between two points is required.

4. Using the Calculator

Tips: Enter the coordinates of both points (x1, y1, x2, y2) as real numbers. The calculator will compute the Euclidean distance between these points.

5. Frequently Asked Questions (FAQ)

Q1: Can this formula be used in 3D space?
A: No, this is the 2D distance formula. For 3D space, the formula extends to: √((x₂-x₁)² + (y₂-y₁)² + (z₂-z₁)²).

Q2: Does the order of points matter?
A: No, the distance is the same regardless of which point is considered first or second because the differences are squared.

Q3: What if I have negative coordinates?
A: The formula works with both positive and negative coordinates as the differences are squared, eliminating sign issues.

Q4: How accurate is the calculation?
A: The calculator provides results with 4 decimal places precision, which is sufficient for most applications.

Q5: Can I use this for geographical coordinates?
A: For small distances on Earth's surface, this can approximate straight-line distance, but for longer distances, the Haversine formula that accounts for Earth's curvature should be used.