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 works with both fractional and decimal coordinates.

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. Importance of Distance Calculation

Details: Distance calculations are fundamental in geometry, physics, computer graphics, and many engineering applications where spatial relationships matter.

4. Using the Calculator

Tips: Enter coordinates as fractions (e.g., 1/2, 3/4) or decimals. The calculator will automatically handle the conversion and computation.

5. Frequently Asked Questions (FAQ)

Q1: Can I use mixed numbers like 1 1/2?
A: Currently only simple fractions (a/b) or decimals are supported. Convert mixed numbers to improper fractions first.

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

Q3: What coordinate system is this for?
A: This works for Cartesian coordinates in 2D Euclidean space.

Q4: Can I use negative fractions?
A: Yes, the calculator handles negative coordinates correctly.

Q5: How precise are the results?
A: Results are rounded to 4 decimal places for readability while maintaining reasonable precision.