Explain why negative reciprocals always have a product of -1?
回答 (3)
2015-11-21 1:45 am
A pair or reciprocals product is always 1 because a reciprocal is 1 divided by a number.
A negative times a positive is a negative.
A negative times a positive is a negative.
2015-11-21 1:31 am
Let a/b be the first slope. Let -b/a be the negative reciprocal. (We assume that a≠0 and b≠0).
The product is:
a .. -b ... -ab
-- x --- = ------ = -1
b ... a .... ab
The product is:
a .. -b ... -ab
-- x --- = ------ = -1
b ... a .... ab
2015-11-21 1:33 am
That's pretty much the definition of a negative reciprocal.
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