Write four pairs of integers which are at the same distance from 2 on the number line.
(1, 3), (0, 4), (−1, 5), (−2, 6)
Explanation (step by step):
On a number line, the distance between two numbers is the absolute value of their difference.
We want two numbers that are the same distance from (2). Such pairs can be made as ((2-k,, 2+k)), where (k) is a positive integer.
Take (k=1).
Left number: (2-1=1)
Right number: (2+1=3)
Distances: (|1-2|=1) and (|3-2|=1)
Pair: ((1,,3))
Take (k=2).
Left number: (2-2=0)
Right number: (2+2=4)
Distances: (|0-2|=2) and (|4-2|=2)
Pair: ((0,,4))
Take (k=3).
Left number: (2-3=-1)
Right number: (2+3=5)
Distances: (|-1-2|=3) and (|5-2|=3)
Pair: ((-1,,5))
Take (k=4).
Left number: (2-4=-2)
Right number: (2+4=6)
Distances: (|-2-2|=4) and (|6-2|=4)
Pair: ((-2,,6))
General rule: for any positive (k), the pair ((2-k,,2+k)) is equidistant from (2).
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