Definition·D070
Difference of two points
Subtract two points of the coordinate plane componentwise.
For
, write
and
, and define
In words
The difference of two points is formed by subtracting their coordinates one at a time.
Rests onno axioms yet
Never needed: F02 · F03 · F04 · F05 · F06 · F08 · F09 · F10 · F11 · F12 · F13 · F14 · A01 · A02 · A03 · A04 · A05 · A06 · A07 · A08 (computed from the citation graph, not asserted).
Remarks
Well defined since
determine
uniquely (the characteristic property of ordered pairs).
is the displacement from
to
; used to build squared distance and the orthogonality hypothesis of the Pythagorean theorem.