1. What is the Distance Formula?

The distance formula calculates the straight-line distance between two points in a coordinate plane. It's derived from the Pythagorean theorem and is fundamental in geometry, physics, and many applied sciences.

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

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 the Distance Formula

Details: The distance formula is used in various fields including computer graphics, navigation systems, physics for calculating displacement, and in mathematics for determining distances between points in 2D and 3D space.

4. Using the Calculator

Tips: Enter the coordinates of two points in the coordinate plane. The calculator will compute the straight-line distance between them. All coordinate values can be positive, negative, or zero.

5. Frequently Asked Questions (FAQ)

Q1: Can this formula be used in 3D space?
A: The 2D distance formula can be extended to 3D by adding a z-coordinate term: \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2}\)

Q2: What if my points have the same coordinates?
A: If both points have identical coordinates, the distance between them will be zero.

Q3: Does the order of points matter?
A: No, the distance is the same regardless of which point is considered first because the differences are squared.

Q4: Can this calculate distances on a map?
A: For small distances on flat maps, yes. For large distances on Earth's curved surface, more complex formulas like the Haversine formula are needed.

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