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 works for any two points (x₁, y₁) and (x₂, y₂).

2. How Does the Calculator Work?

The calculator uses the distance formula:

Where:

• \( (x_1, y_1) \) — Coordinates of first point
• \( (x_2, y_2) \) — Coordinates of 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 Distance Calculation

Details: The distance formula is fundamental in geometry, physics, computer graphics, navigation systems, and many engineering applications where measuring spatial relationships is important.

4. Using the Calculator

Tips: Enter the coordinates of two points in the plane. The calculator accepts any real numbers (positive, negative, or zero) and provides the distance in the same units as the coordinates.

5. Frequently Asked Questions (FAQ)

Q1: Does the order of points matter?
A: No, the distance is the same whether you calculate from (x₁,y₁) to (x₂,y₂) or vice versa because the differences are squared.

Q2: Can this be used for 3D coordinates?
A: This calculator is for 2D coordinates only. For 3D, the formula extends to include the z-coordinate: √[(x₂-x₁)² + (y₂-y₁)² + (z₂-z₁)²].

Q3: What if I get a negative distance?
A: Distance is always non-negative. If you see a negative result, check your calculator inputs as this indicates an error.

Q4: How precise are the results?
A: Results are rounded to 4 decimal places. For most practical applications, this provides sufficient precision.

Q5: Can I use this for geographical coordinates?
A: For small distances on Earth's surface, this works as an approximation. For larger distances, you would need to account for Earth's curvature using the haversine formula.