Ray has a starting point but it goes upto
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INFINITY
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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.
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