1. What is the Distance Formula?

The distance formula calculates the straight-line distance between two points in a Cartesian coordinate system. It is derived from the Pythagorean theorem and is fundamental in geometry, physics, and various engineering applications.

2. How Does the Calculator Work?

The calculator uses the distance formula:

Where:

• \( D \) — Distance between the two points
• \( x_1, y_1 \) — 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: Distance calculation is essential in navigation, computer graphics, physics, engineering, and many scientific fields where spatial relationships between points need to be quantified.

4. Using the Calculator

Tips: Enter the coordinates of both points in the Cartesian coordinate system. The calculator accepts any real number values for coordinates.

5. Frequently Asked Questions (FAQ)

Q1: Can this formula be used in 3D space?
A: No, this formula is specifically for 2D space. For 3D space, the formula extends to: \( D = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2} \)

Q2: What if my points have negative coordinates?
A: The formula works with both positive and negative coordinates as the differences are squared, eliminating any negative signs.

Q3: How accurate is the calculation?
A: The calculator provides results with up to 4 decimal places, but the actual precision depends on the input values.

Q4: Can I use this for geographical coordinates?
A: No, for geographical coordinates (latitude and longitude), you need to use the Haversine formula which accounts for the Earth's curvature.

Q5: What units does the result use?
A: The result is in the same units as the input coordinates. If you input coordinates in meters, the distance will be in meters.