1. What is the Distance Formula?

The distance formula calculates the length between two points in a 2D plane. It's derived from the Pythagorean theorem and is fundamental in geometry and coordinate systems.

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.

3. Importance of Line Segment Length

Details: Calculating distances between points is essential in geometry, physics, engineering, computer graphics, and many other fields that deal with spatial relationships.

4. Using the Calculator

Tips: Enter the coordinates of two points in the plane. The calculator will compute the straight-line distance between them. Works with any consistent units (meters, feet, pixels, etc.).

5. Frequently Asked Questions (FAQ)

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

Q2: How does this relate to Desmos?
A: Desmos is a graphing calculator that can visualize line segments and automatically calculate their lengths using this formula.

Q3: Can this be extended to 3D?
A: Yes, the 3D distance formula adds a z-coordinate term: \(\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2 + (z_2-z_1)^2}\)

Q4: What if my points have negative coordinates?
A: The formula works with any real number coordinates, positive or negative.

Q5: How precise are the calculations?
A: The calculator provides results rounded to 2 decimal places, but the actual computation uses more precise internal values.