题干

(1)阅读下面材料:

点A,B在数轴上分别表示实数a,b,A,B两点之间的距离表示为|AB|.

当A,B两点中有一点在原点时,不妨设点A在原点,如图(1),|AB|=|OB|=|b|=|a﹣b|;

当A,B两点都不在原点时,

①如图(2),点A,B都在原点的右边,|AB|=|OB|﹣|OA|=|b|﹣|a|=b﹣a=|a﹣b|;

②如图(3),点A,B都在原点的左边,|AB|=|OB|﹣|OA|=|b|﹣|a|=﹣b﹣(﹣a)=|a﹣b|;

③如图(4),点A,B在原点的两边,|AB|=|OA|+|OB|=|a|+|b|=a+(﹣b)=|a﹣b|;

综上,数轴上A,B两点之间的距离|AB|=|a﹣b|.

(2)回答下列问题:

①数轴上表示2和5的两点之间的距离是____ ,数轴上表示﹣2和﹣5的两点之间的距离是 3 ,数轴上表示1和﹣3的两点之间的距离是____ ;

②数轴上表示x和﹣1的两点A和B之间的距离是____ ,如果|AB|=2,那么x为____ ;

③当代数式|x+1|+|x﹣2|取最小值时,相应的x的取值范围是____ .

④当x=____  时,|x+1|+|x﹣2|=5.

 

上一题 下一题 0.0难度 选择题 更新时间:2019-11-29 11:10:09

答案(点此获取答案解析)

3,4,|x+1|,±2,﹣1≤x≤2 ,3或﹣2 

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