Distance Formula Calculator Geometry

Distance Formula:

\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

Point 1 X-coordinate (x₁):

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Point 1 Y-coordinate (y₁):

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Point 2 X-coordinate (x₂):

units

Point 2 Y-coordinate (y₂):

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Distance (d):

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1. What is the Distance Formula?

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

2. How Does the Calculator Work?

The calculator uses the distance formula:

\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

Where:

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

Explanation: The formula calculates the hypotenuse of a right triangle formed by the differences in x and y coordinates.

3. Applications of the Distance Formula

Details: Used in navigation, computer graphics, physics (calculating displacements), machine learning (similarity measurements), and many other fields.

4. Using the Calculator

Tips: Enter coordinates for two points in any units (must be consistent). The calculator will compute the distance in the same units.

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.

Q2: How does this extend to 3D space?
A: In 3D, the formula becomes \( d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2 + (z_2-z_1)^2} \).

Q3: What if my coordinates are negative?
A: The formula works with any real numbers - negative coordinates are squared so become positive.

Q4: What's the precision of the calculator?
A: It calculates to 4 decimal places, but precision depends on your input values.

Q5: Can I use this for geographic distances?
A: Only for small areas - for large distances you need to account for Earth's curvature.