Definition·D073
Orthogonal points
Two points of the plane, viewed as vectors from the origin, are orthogonal when their dot product is zero.
For
:
with
from D071.
In words
Two points, viewed as vectors from the origin, are orthogonal when their dot product is zero.
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
Read
as "
and
are perpendicular". A triangle with vertices
has a right angle at
exactly when
(D070), the hypothesis of the Pythagorean theorem.