Definition
Point
An exact location in space with no length, width, or thickness.
What it means
Think of a point as an address, not a tiny object. A dot helps us see where the address is, yet the mathematical point has no length, width, or thickness. Points can mark coordinates, endpoints, and vertices.
Remember it
A point is an address; the dot is only its sign.
Example
Point A at (3, 2) marks the location reached by moving 3 units right and 2 units up from the origin.
Watch for
Making the dot larger does not make the point larger; every drawn dot still represents a location with no size.
Common mix-up
Every polygon vertex is a point, but a point along the middle of a side is not a vertex.
Exact meaning
A geometric point is an exact location with no size. A drawn dot and a capital letter represent and name the point, but the ink mark is not the point itself.