keep your distance

keep (one's) distance

To limit engagement or association (or the appearance thereof) between oneself and someone or something. Politicians have been quick to keep their distance from the senator ever since news of her drug scandal broke. That kid needs to keep his distance—I'll call the police if I catch anyone trespassing on my property.
See also: distance, keep

keep your ˈdistance (from somebody/something)

,

keep somebody/something at a ˈdistance

not be too friendly or familiar with somebody/something: She tends to keep her distance from her neighbours, so none of them know her very well.
See also: distance, keep
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