WHEN BETHESDA’S Katie Ledecky, 15, jumped into the pool in Omaha on Sunday, she was aiming to become the youngest member of the U.S. swim team. Eight minutes, 19.78 seconds and 800 meters later, Ledecky’s left hand touched the wall, her right arm pumped triumphantly in the air, and a smile spread across her youthful face. Ledecky had punched her ticket for London and the 2012 Olympic Games.

Then Ledecky leaned across the lane barrier to embrace second-place finisher Kate Ziegler, a 24-year-old Great Falls native whose renewed passion for swimming helped her secure a return trip to the Olympics. The pair will join Matt McLean, a Sterling native and University of Virginia graduate, as swimmers representing the metropolitan area at the Games. Ledecky and Ziegler will compete in the 800-meter women’s freestyle, while McLean, 24, will swim in the 800-meter men’s freestyle relay.

Ledecky, Ziegler and McLean’s Olympic berths add to a long history of success for local swimmers on the national and international levels. The trio competes for Potomac Valley Swimming, the governing body for swimming in the metro area. Despite its status as, geographically, the smallest swimming community in the country, Potomac Valley has the fifth largest membership. A Potomac Valley swimmer has appeared in every Olympic Games but one since 1988.

Ledecky, a rising sophomore at Stone Ridge,qualified for the Games one day after narrowly failing to make the team in the 400-meter freestyle — an event in which she still broke Janet Evans’s 24-year-old national record for the 15- and 16-year-old age group. Now that she’s past the trial stage, she can turn her focus to success in London: “I just want to represent the U.S. to the best of my ability and see if I can drop some more time,” Ledecky said. “Then hopefully I’ll be in position for a good finish.”

Ziegler will be returning to the Olympics after a disappointing debut four years ago in Beijing, where she placed 10th and 14th, respectively, in the 800 and 400 freestyle events. This year, she has a new responsibility on the national team: guiding Ledecky through her first Olympics. “I would love to be able to leave the sport saying that I helped mentor or shape or whatever, give advice to the future of our sport,” Ziegler told The Post’s Amy Shipley. “I think that’s one of the greatest gifts I could ever give.”

With their accomplishments in Omaha, Ledecky, Ziegler and McLean already have given those in the D.C. area much to be proud of. In just over three weeks, they will try to build on their efforts in the Olympic Trials and bring gold home to the region. They will be well worth watching.