Measure the straight-line separation between two points in a coordinate plane. The page traces how the inputs become distance before rounding.
Review x₁ inside the Distance Formula relation. Hold y₁ steady while testing x₂. A rough Distance gives Distance Formula an independent scale check. Keep the revised Distance Formula inputs beside their own Distance.
Coordinate distance is used in analytic geometry, mapping on flat grids, screen layouts, and vector calculations. It represents the direct segment, not a route constrained to horizontal and vertical streets.
Subtract x-coordinates and y-coordinates, square both differences, add the squares, and take the nonnegative square root. Keep radical form if an exact result is requested.
The order of points does not matter, but each coordinate must remain paired with its own point. On the Earth's curved surface, latitude and longitude require a spherical or ellipsoidal distance model instead. If the Distance Formula assumptions do not fit, consider right-triangle relation.
Between (−2, 4) and (5, −1), horizontal change is 7 and vertical change is −5. Distance is √(7² + (−5)²) = √74, approximately 8.6023. This Distance Formula example can be compared with directional steepness.
The Distance Formula meaning depends on x₁. The Distance Formula meaning also depends on y₁. Carry those Distance Formula roles into any later Distance Formula work.
The coordinate distance formula is the Pythagorean theorem applied to horizontal and vertical changes. Squaring removes direction and the final square root restores the original unit. For a connected concept in Distance Formula, see center of the segment.
An independent estimate makes Distance Formula easier to trust. Derive a rough Distance from x₁ and y₁, then compare its magnitude with the calculated Distance. Large disagreement deserves attention before the Distance Formula output is rounded or reused.
No. Geometric length is nonnegative.
No. Reversing the order negates both differences, but their squares stay the same.
No. It is Euclidean straight-line distance.
Both coordinate changes are zero, so the distance is zero.
The result uses the same coordinate unit; label it when the coordinates represent physical measurements.