Turn Coordinate Changes into Length

Coordinates describe position; differences describe movement

An ordered pair (x,y) locates a point relative to an origin and two perpendicular axes. A coordinate is not itself a distance between two arbitrary points. From A(x₁,y₁) to B(x₂,y₂), calculate Δx=x₂−x₁ and Δy=y₂−y₁ in the same endpoint order. A negative change means movement left or down; a length is nonnegative. Moving horizontally and then vertically creates a right triangle whose legs have lengths |Δx| and |Δy|. Coordinates must use the same length scale on both axes before the usual formula gives a physical distance.