half-line

A student draws a half-line on the chalkboard.

Definition

1. Noun:
   • A straight line extending infinitely in one direction from a point: In geometry, a "half-line" (also called a ray) is a set of points that begins at a specific point (the endpoint) and continues without end in a single direction.
   • A line segment of indefinite length: In less formal usage, it may refer to a line that has a starting point but no defined endpoint.

Usage Examples

• Noun:
  • The student drew a half-line from point A through point B. (A geometric ray starting at A and passing through B.)
  • In coordinate geometry, a half-line is often represented as a vector with an initial point. (A mathematical construct with a fixed start and infinite extension.)

Advanced Usage

• "half-line in projective geometry": In projective geometry, a half-line is a line with a designated direction, used to define oriented angles.
  • The concept of a half-line is fundamental to understanding directed angles in Euclidean space. (It helps describe angular relationships with orientation.)

Variants and Related Words

• Ray (n): a synonym for half-line in mathematics.

  • A ray is a half-line that starts at a point and extends infinitely in one direction. (An alternative term used interchangeably.)

• Line segment (n): a part of a line that has two endpoints, distinct from a half-line.

  • Unlike a half-line, a line segment has a finite length. (A different geometric object with both ends fixed.)

Synonyms

• Ray: a straight line extending from a point.
• Directed line: a line with a specified starting point and direction.

Related Idioms

• There are no common idioms using "half-line" in everyday English; it is primarily a technical term in mathematics and geometry.