1. What is the 2D Distance Formula?

The 2D distance formula calculates the straight-line distance between two points in a Cartesian plane. It's derived from the Pythagorean theorem and is fundamental in geometry, physics, and many engineering applications.

2. How Does the Calculator Work?

The calculator uses the 2D distance formula:

Where:

• \( d \) — Distance between points (units)
• \( x_1, y_1 \) — Coordinates of first point (units)
• \( x_2, y_2 \) — Coordinates of second point (units)

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: Used in computer graphics, navigation systems, physics simulations, game development, and any application requiring spatial measurements.

4. Using the Calculator

Tips: Enter coordinates for both points in the same units. The calculator works with any real numbers (positive or negative).

5. Frequently Asked Questions (FAQ)

Q1: Does the order of points matter?
A: No, distance is the same regardless of which point is first because differences are squared.

Q2: What if my points have negative coordinates?
A: The formula works with any real numbers - negative coordinates are handled automatically.

Q3: How precise is the calculation?
A: The calculator shows results rounded to 2 decimal places, but uses full precision for calculations.

Q4: Can this be extended to 3D space?
A: Yes, the 3D distance formula adds a z-coordinate term: \( \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2 + (z_2-z_1)^2} \)

Q5: What units should I use?
A: Any consistent units (meters, feet, pixels, etc.) as long as both points use the same units.