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

• A. Manhattan distance
• B. Chebyshev distance
• C. Haversine distance
• D. Euclidean distance

Answer: (D)

Euclidean distance is the straight-line distance between two points in Euclidean space. It comes from the Pythagorean theorem: in two dimensions, distance = sqrt((x2 − x1)² + (y2 − y1)²); in n dimensions, distance = sqrt(sum_i (p_i − q_i)²). This is the “as the crow flies” measure of separation.

The other options describe different ideas of distance: Manhattan distance sums the absolute differences along each axis, reflecting grid-like movement; Chebyshev distance uses the maximum axis difference, like the number of moves a king would need on a chessboard; Haversine distance calculates great-circle distance on a sphere, which accounts for Earth's curvature rather than straight-line Euclidean space.