1. What is the Pythagorean Theorem?

The Pythagorean Theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. This calculator applies this theorem to calculate the distance between two points in a 2D plane.

2. How Does the Calculator Work?

The calculator uses the distance formula derived from the Pythagorean Theorem:

Where:

• \( (x_1, y_1) \) — Coordinates of the first point
• \( (x_2, y_2) \) — Coordinates of the second point
• \( c \) — Distance between the two points

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

3. Applications of the Pythagorean Theorem

Details: This calculation is fundamental in geometry, physics, engineering, computer graphics, navigation, and many other fields where distance measurements are needed.

4. Using the Calculator

Tips: Enter the coordinates of two points in any unit (they must be consistent). The calculator will compute the distance between them in the same units.

5. Frequently Asked Questions (FAQ)

Q1: Does this work for 3D coordinates?
A: This calculator is for 2D points only. For 3D points, you would need to extend the formula to include the z-coordinate.

Q2: What if my points have negative coordinates?
A: The formula works for all real numbers - negative coordinates are handled correctly by the subtraction and squaring operations.

Q3: How accurate is this calculation?
A: The calculation is mathematically exact for the given coordinates. Rounding only occurs in the displayed result.

Q4: Can I use different units for x and y coordinates?
A: No, both coordinates must be in the same units for the distance result to be meaningful.

Q5: What's the maximum distance this can calculate?
A: There's no theoretical maximum, but extremely large values might encounter floating-point precision limitations.