# Concept derivation guides

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Concept guide



## [Euclidean length: computing the distance between two points exactly from coordinates](/en/derivations/derivation-mko-euclidean-length-01/?from=%2Fen%2Fderivations%2F%3Fq%3Dmko-euclidean-length)

In the Euclidean plane represented by ℝ², let P=(1,−2), Q=(4,2), R=(2,3). Compute d(P,Q)=5 exactly; compute d(P,R)=√26 and prove by comparing squares that 5.09<√26<5.1, showing that 5.1 is only an approximation. For general real coordinates, also prove that the distance is defined and nonnegative, that d(Q,P)=d(P,Q), that d(P,P)=0, and that d(P,Q)=0 ⇔ P=Q.

Euclidean length

derivation-mko-euclidean-length-01





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