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 provides the shortest path between any two points in 2D space.

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
• \( \sqrt{} \) — Square root function

Explanation: The formula calculates the horizontal and vertical differences between the points, squares them, sums the squares, and takes the square root to find the straight-line distance.

3. Importance of Distance Calculation

Details: Distance calculation is fundamental in mathematics, physics, engineering, computer graphics, navigation, and many real-world applications like GPS systems, game development, and architectural planning.

4. Using the Calculator

Tips: Enter the coordinates of both points in the same unit system. The calculator accepts decimal values for precise calculations. The result will be in the same units as your input coordinates.

5. Frequently Asked Questions (FAQ)

Q1: Can this calculator handle negative coordinates?
A: Yes, the calculator works with both positive and negative coordinates as the formula squares the differences, eliminating sign issues.

Q2: What coordinate system does this use?
A: This uses the standard Cartesian coordinate system with x and y axes.

Q3: Can I use this for 3D coordinates?
A: No, this calculator is specifically for 2D coordinates. For 3D distance, you would need to add a z-coordinate term.

Q4: How accurate are the results?
A: Results are accurate to 2 decimal places, but you can input coordinates with up to 4 decimal places for precision.

Q5: What units should I use?
A: You can use any consistent units (meters, feet, pixels, etc.). The result will be in the same units as your input coordinates.