Tendu is one of the French words for ballet. It means stretched. Usually, that means you have pointed your foot in a front, side, or backward direction from a closed position. Whether in soft ballet shoes or pointe shoes, the technique is the same. Tendu prepares the muscles for releve and saute.
Whether you pick up a ballet glossary at a ballet store, or find one on line, every new student needs one. Even if you speak French, the way the words are used can be different.
Battement tendu is a movement opening the foot and leg, keeping the pointe of the toes on the floor.
Assuming that your posture is correct, "spine neutral", your turnout is from the hips, your neck and shoulders are relaxed, and your barre arm is resting lightly, not too much happens!
True, and not true.
If your are in fifth position, you begin shifting the weight to the standing leg and sliding the working heel forward, at the same time. You are pressing your heel forward, if you are going devant - to the front, or a la seconde, to the side. You can turn out your foot because you are taking the weight off that leg, so there is no strain on the knee joint.
Here's a tricky part - as you extend the leg, you keep pressing the foot into the floor. Not so as to strain the knee joint with having weight on the foot - no, but you are creating resistance. You press the foot into the floor to build strength in the foot muscles. You do not curl your toes to do this, think of the whole foot. But as you are extending the foot to the position, this happens quickly. After the metatarsal area has left the floor, be sure to stretch your toes out long, do not curl or bend them. The movement is over when the arch is fully stretched, and the toes simply come into line.
***This is the same movement you will do in pointe shoes, keeping the toes long, not bent over.***
Some techniques teach that you extend the foot so that the toes end up opposite the standing heel, in a devant position. Others teach that you cross the foot over so that the toe ends up opposite the center of the standing foot, or in line with the center of the torso. You can lose turnout crossing over like this, or, keeping the turnout, you can end up losing the hip placement, turning the body slightly croise (toward the corner of the supporting side). In the early years of training I see no reason not to stay with the extended toes in line with the supporting heel.
If nothing else has happened in the body, you have done a correct tendu devant.
To close, you relax your toe joints, pressing the toes slightly into the floor as the leg draws in, the toes pull back, the heel lowers, until the sole of the foot is pressing on the floor. Here's the little tricky area again - you pull the leg in, but you must stop pulling the toes back as you get into fifth (or first) so as not be turning the foot out too much. You have to stand on the whole foot, turned out from the hip rotators. Ballet is not anatomically correct, but you must compromise without injuring your knees, rolling your ankles, and being off balance.
At the end of the movement, your weight must be evenly on two feet, hips square, spine still neutral, neck relaxed. With the thousands of tendus you do in ballet training, there is no way you will not get strong and build good dance technique.