NEW YORK — ATA Airlines Inc.'s plan to sell its defunct business to Southwest Airlines Co. was formally approved by a judge, allowing it to liquidate almost a year after high fuel costs drove the carrier into bankruptcy.

The plan, approved March 26 by U.S. Bankruptcy Judge Basil Lorch in Indianapolis, where ATA is based, pays about 1.3 percent on unsecured claims totaling roughly $420 million and about 13.9 percent on secured claims of $365 million, court papers show.

Southwest, the largest low-fare airline, won court approval in December to buy ATA assets including 14 flight slots at New York's LaGuardia airport for $7.5 million. Low-fare carrier AirTran Holdings Inc. agreed in January to buy ATA's two flight slots at Washington's Reagan National airport for $1.34 million.

ATA flew 29 aircraft to destinations including Hawaii and Mexico before it sought bankruptcy protection in April 2008 and ceased operations. Out of at least seven carriers that filed for bankruptcy last year, only Frontier Airlines Inc. and Sun Country Airlines are still operating. ATA's operations won't be revived.