Why are ray AC and ray BA not opposite rays?

Conditions

• The rays are named $\overrightarrow{AC}$ and $\overrightarrow{BA}$.
• Points A, B, and C are on a line.

Reasoning, step by step

1. Identify the endpoint of $\overrightarrow{AC}$, which is A.
2. Identify the endpoint of $\overrightarrow{BA}$, which is B.
3. Compare the endpoints: A is not equal to B.
4. Conclude that since they do not share a starting point, they cannot be opposite rays.

Example

The instructor sketches a line with points A, B, C and explains: 'You wouldn't want to do ray AC and ray BA because then they don't have the same starting point.'

Common misconceptions

• Assuming that just because the rays point in opposite directions, they are opposite rays.
• Ignoring the requirement for a common endpoint.

Watch the explanation

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