Which distance metric is defined as the straight-line distance in Euclidean space between two points?

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Multiple Choice

Which distance metric is defined as the straight-line distance in Euclidean space between two points?

Straight-line distance in ordinary Euclidean space is measured by the Euclidean distance. In two dimensions it follows the Pythagorean formula sqrt((x1 - x2)^2 + (y1 - y2)^2); in higher dimensions you take the square root of the sum of the squared differences across all coordinates. This represents the direct length of the line connecting the two points, regardless of any grid or axis-aligned paths. Other metrics describe distance in different ways: Manhattan distance sums the absolute differences along each axis, Chebyshev distance takes the largest single coordinate difference, and Hamming distance counts how many positions differ between equal-length vectors. So, the distance that embodies the straight-line concept is the Euclidean distance.

Straight-line distance in ordinary Euclidean space is measured by the Euclidean distance. In two dimensions it follows the Pythagorean formula sqrt((x1 - x2)^2 + (y1 - y2)^2); in higher dimensions you take the square root of the sum of the squared differences across all coordinates. This represents the direct length of the line connecting the two points, regardless of any grid or axis-aligned paths. Other metrics describe distance in different ways: Manhattan distance sums the absolute differences along each axis, Chebyshev distance takes the largest single coordinate difference, and Hamming distance counts how many positions differ between equal-length vectors. So, the distance that embodies the straight-line concept is the Euclidean distance.

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