"what is the name of the ray that is opposite of ray ba?

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Think of a ray as a line that has one endpoint on one side, and the other side extends indefinitely in one direction. Opposite rays will have the same endpoint and extend in opposite directions. Rays are always named with two points and the first point in the name must be the endpoint. So, the name of the ray opposite of BA will be BC. B is the shared endpoint between the two.