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Three collinear points don't define a plane."Define" means narrow it down to one and only one unique plane, so that it can't be confused with any other one.There are many different planes (actually infinite) that can contain three collinear points, so no unique plane is defined.
It is sometimes called the pre-image.
In plane geometry, two points determines or defines one unique line.
The shape described is a plane, which is a two-dimensional surface that extends infinitely in both width and length. In geometry, a plane can be uniquely determined by any three non-collinear points on the plane. This is known as the "three-point" or "unique determination" property of a plane. The three points define the plane's orientation and position in three-dimensional space.
A coordinate plane! If it has one or more breaks in it is not a coordinate plane but only a part of one.