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A good approach shot makes it more difficult for your opponent to hit a successful passing shot and easier for you to put your volley away. You'll usually hit an approach shot when your opponent sends you a somewhat short ball. If the ball is only moderately short, you can choose whether to hit an approach shot and come in or to hit an aggressive groundstroke and then move back to a baseline position. If the ball is so short that you wouldn't have time to get set up back at your baseline, you'll have to advance toward the net, and only a groundstroke winner or a good approach shot will allow you to keep the advantage. Sending your opponent an easy ball when you're approaching the net usually results in getting passed or lobbed.
If your approach shot is deep and hard, very low, far from your opponent, low and short, or deep and high-bouncing, it will probably set you up for an easy volley. Each opponent will be vulnerable to particular approach shots. Most one-handed backhanders, for example, will have trouble with high bounces on the backhand side. Most two-handed backhanders and Western forehanders will find low, slightly short balls difficult. It's always smart to try the full range against an opponent and see what works, then keep mixing your strokes so that she can't get used to your attacks.
Approach shots should generally be hit down the line, because this puts you closer to the center of the passing shot angles your opponent might hit. If your opponent is significantly weaker on one side than the other, though, it can be worth hitting to that weak side even if it's crosscourt. You'll have farther to move to get into good volleying position, but a poor passing shot will still be easy to put away.
The slow-motion video on the next page nicely illustrates the flow of a smooth approach shot.