How did balançoire get its name? The answer lies in visualizing the movement and the line created by the swing of the upper and lower body as it moves on the fulcrum of the supporting hip.
Today balançoire can refer to either a seesaw or a swing, seesaw being the more ancient of these two references, but swing being the more common. In either of these pieces of playground equipment, we can find the line of the ballet balançoire.
Balançoire is prounounced [balɑ̃swaʀ]. Bal- is pronounced like the beginning of the word ballet in English. (The English is not far from the French in this case. The English pronunciation would pull the corners of the mouth back at the vowel, while the French would keep the mouth slightly rounder and more open.) -an- would be like “ah” but with sound passing through both the mouth and nose since this is a nasal vowel (the n not a clear n sound as it would be in English). -çoire is proncounced “sw” + “are.”
The action of balançoire takes place both above and below the waist. As the dancer’s leg brushes forward in a battement (dégagé or grand battement for example) the torso tips back. The dancer’s leg can then pass through first position traveling to the back. As the leg travels back, the dancer’s torso tips forward. The movement of the working leg is similar to that of battement cloche, but balançoire incorporates the tip of the torso.
When the leg is kept at a low height, dancers can visualize a swing on a chain. Imagine the top of the head as the top of the chain and picture the straight line extending down through the working leg to the low extension. Because the upper body moves in opposition of the working foot, a dancer can imagine the swing arcing from front to back. With a high leg, I prefer the image of a seesaw with the supporting hip acting as the fulcrum of the seesaw, but you can certainly keep the swing imagery if you imagine that the leg swings from front to back or back to front or that the body takes the position of a person seated on a swing. As the leg swings forward the leg is outstretched and the upper body tipped back as it would be when seated on a swing, however, I find this imagery less convincing in arabesque.