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A half-line is just a set of the form $a + tb$ for $t \ge 0$, in a vector space over the reals. In the plane this just amounts to lines that are "cut off", i.e. have an endpoint, but then extend towards infinity.
A ray is occasionally referred to as a half line. Rays begin at one point and continue indefinitely in a single direction after passing through another point (reference illustration below): Similar to the methodology described above, a single arrowhead overbar is used to denote a ray. Accordingly, the ray above may be denoted as:
Rays (or half-lines) the same as lines are designated by lowercase Latin letters: ray a or ray b. A half-line (or ray) is also designated by two points: the initial point and another point belonging to the half-line. In doing so, the initial point is placed in the first place.
In geometry, a half-space is either of the two parts into which a plane divides the three-dimensional Euclidean space. If the space is two-dimensional, then a half-space is called a half-plane (open or closed). A half-space in a one-dimensional space is called a half-line or ray.
A ray is defined by two points on the line; the first point is where the ray begins, and the second point gives the line direction. A half-line is defined by two points, one where the line starts and the other to give direction, but an open circle at the starting point indicates that the starting point is not part of the half-line.
10 paź 2024 · When viewed as a vector, a ray is a vector AB^-> from a point A to a point B. In geometry, a ray is usually taken as a half-infinite line (also known as a half-line) with one of the two points A and B taken to be at infinity.
Course: Geometry (all content) > Unit 1. Lesson 1: Lines, line segments, and rays. Euclid as the father of geometry. Terms & labels in geometry. Lines, line segments, & rays. Identify points, lines, line segments, rays, and angles. Identifying rays. Draw rays, lines, & line segments.
