For these shots, I used a Fuji X100T and used a cheap, no-named radio trigger with a Nikon SB-800 set to non-TTL automation. Depending on the intensity of the existing light, I sometimes decreased the flash output by decreasing the size of the aperture.
Zone Focusing: Here's a technique that can be applied in situations were your camera is having difficulty keeping up with the rapid movement of the dancers. Instead, I set the camera my X100 T to Manual Focus, and using the distance scale displayed in the viewfinder, chose a distance of 5 feet. Now all I have to do is stand 5 feet from my main subject and shoot when I get the expression I want. It can get tricky, but I learned to move forward and backward with my subjects in an attempt to keep the distance as close to 5 feet as I could (Photo #3).
The more I thought about it, the more I realized that I had used the zone focusing technique many, many years ago, when lenses focused manually and every lens had a distance scale and depth of field markers. Having essentially the same features on my Fuji made it pretty easy to apply this old technique.