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Mathematical number axis problem
1。 It is known that points A and B on the number axis represent two numbers A and B (a

Solution: A and B are opposites, then

a+b=0,.....................( 1)

The AB distance is 6, then

b-a=6......................(2)

Solve (1)(2) simultaneously.

a=-3,b=3

2. It is known that the distance between the point M representing the number A and the point representing the number-1 on the number axis is 3, and the distance between the point N representing the number B and the point representing the number 2 is 4. Find the distance between m and n.

Solution: If the distance between the point M representing the number A and the point representing the number-1 on the number axis is 3, then

A=2 or -4

The distance between the point n representing the number B and the point representing the number 2 is 4, so

B=6 or -2

So the distance between m and n is 2 or 4 or 10.

(The last three values are because when a=2, the distance is 4; When a=-4, the distance is 10 or 2. )