What is a ray in geometry?

In geometry, a ray is a part of a line that has one endpoint and extends infinitely in one direction. Here's a breakdown of its key characteristics:

• One Endpoint: Unlike a line, which extends infinitely in both directions, a ray has a starting point, called its endpoint or origin.

• Infinite Length in One Direction: From its endpoint, it continues infinitely in a single direction. You can think of it as half of a line.

• Notation: Rays are typically denoted using two points. The first point is the endpoint, and the second point is any other point on the ray. For example, if the endpoint is A and another point on the ray is B, the ray is denoted as →AB (or sometimes just AB with an arrow above). The arrow indicates the direction the ray extends infinitely. Note that →AB is not the same as →BA; they are opposite rays.

• Collinear Rays: If two or more rays share the same endpoint and lie on the same line, they are called collinear rays. Opposite rays are a special case of collinear rays.

• Opposite Rays: Two rays that share the same endpoint and extend in opposite directions are called opposite rays. They form a line.

• Applications: Rays are fundamental to many geometric concepts, including angles (formed by two rays sharing a common endpoint), and are crucial in various fields like computer graphics (representing light beams) and physics (describing the propagation of waves).

In essence, a ray is a one-dimensional object extending infinitely in only one direction from a fixed point.