Why is the receiver’s partner standing up at the net just behind the kitchen line?

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It is a strategic position, not a rule, the receiver’s partner should stand behind the kitchen line (or non-volley line) to keep an eye on the serve and help call the ball if it's out of play.  You can also defend the line.

In doubles, there’s no rule on the position of any player with the exception of the server, which must serve from behind the line.

Players can position themselves anywhere as long as they are on their respective side of the court.

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ENGAGE