Question #9089
Points A, B, and C are noncollinear. How many planes can be determined by A, B, and C?
Expert's answer
In 3-dimensional space if the points A, B, and C are noncollinear, i.e. do not
belong to the same line,
then there exists a UNIQUE plane passing through
these points.
Therefore AB and AC are distinct lines.
Therefore by one
of axioms of elementary geometry, these lines determine a unique plane.
belong to the same line,
then there exists a UNIQUE plane passing through
these points.
Therefore AB and AC are distinct lines.
Therefore by one
of axioms of elementary geometry, these lines determine a unique plane.
