Definition: A portion of a line which starts at a point and goes off in a particular direction to infinity.
Adjust the ray below by dragging an orange dot and see how the ray
AB behaves. Point A is the ray's endpoint.
One way to think of a ray is a line with one end.
A ray starts at a given point and goes off in a certain direction forever, to infinity.
The point where the ray starts is called (confusingly) the endpoint.
On its way to infinity it may pass through one or more other points. In the figure above, the ray starts at A and also passes through B.
A ray is one-dimensional. It has zero width. If you draw a ray with a pencil, examination with a microscope would show that the pencil mark has a measurable width. The pencil line is just a way to illustrate the idea on paper. In
geometry however, a ray has no width.
A ray has no measurable length, because it goes on forever in one direction.
Drawing a ray
You can draw a ray as a line that just goes off the edge of the page, as in the figure above.
More commonly it shown as a line with an arrow head on one end as shown below.
The arrow head means that the line goes off to infinity in that direction.
Naming of rays
Rays are commonly named in two ways:
- By two points.
In the figure at the top of the page, the ray would be called AB because starts at point A and
passes through B on its way to infinity.
Recall that points are usually labelled with single upper-case (capital) letters.
There is a shorthand way of writing this:
This is read as "ray AB".
The arrow over the two letters indicates it is a ray, and the arrow direction indicates that A is the point where the ray starts.
- By a single letter.
The ray above would be called simply "q".
By convention, this is usually a single lower case (small) letter.
This is normally used when the ray does not pass through another labeled point.
In another branch of mathematics called coordinate geometry, the points that define a ray are located on the plane using their
coordinates - two numbers that show where the point is positioned.
For more on this, see Ray definition (Coordinate Geometry).
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