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A generatrix is an element of a set of straight lines which constitute a given surface.

Generatrix of Right Circular Cone

Let $K$ be a right circular cone.

Let $A$ be the apex of $K$.

Let $B$ be the base of $K$.

Then a line joining the apex of $K$ to its directrix is a generatrix of $K$.

Also known as

A generatrix of a surface can also be referred to as a generator or generator element.

Linguistic Note

The word generatrix is the feminine form of the word generator.

As such, the form is archaic, and is rarely (if ever) found outside the context of mathematics.