1. What Is The Distance Formula?

The distance formula is derived from the Pythagorean theorem and calculates the straight-line distance between two points in a Cartesian coordinate system. It's a fundamental concept in geometry and coordinate mathematics.

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. Applications Of Distance Calculation

Details: The distance formula has wide applications in mathematics, physics, engineering, computer graphics, navigation systems, and geographic information systems (GIS).

4. Using The Calculator

Tips: Enter the coordinates of two points in the Cartesian plane. The calculator will compute the straight-line distance between them. All coordinate values can be positive, negative, or zero.

5. Frequently Asked Questions (FAQ)

Q1: Can this formula be used in 3D space?
A: No, this is specifically for 2D coordinates. 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, as the differences are squared.

Q3: What units does the result use?
A: The result is in the same units as the input coordinates. If coordinates are in meters, the distance will be in meters.

Q4: Can I calculate distance between geographic coordinates?
A: This formula works for Cartesian coordinates. For geographic coordinates (latitude/longitude), you need the Haversine formula which accounts for Earth's curvature.

Q5: What's the maximum precision of the calculation?
A: The calculator uses floating-point arithmetic with 4 decimal places precision, suitable for most applications.