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They are opposite if a + (-A) = 0

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Q: How do you know te expressions a and -A represent opposite distances?
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How do you know the expressions A and -A represent opposite distances?

Both have magnitudes of A, so they are equal distances and, by the definition of additive inverses, A + (-A) = 0 and that means that they are opposite. Of course, they need not be opposite distances: they could be opposite times, or opposite amounts of money.


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