At around 5 a.m., officers received a 911 call about an assault in progress at a home in Far Rockaway in Queens.
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Officers on patrol responded to the location and approached a man they say was leaving the driveway of the residence with luggage.
Police say the man, identified as Courtney Gordon, 38, encountered responding officers in the street and slashed two of them with a kitchen knife, before officers fatally shot him.
When officers arrived at the home, they found an 11-year-old girl lying on the ground outside the residence. She was taken to a hospital, where she was pronounced dead.
Officers say the man set fire to a couch in the living room, which made it difficult for them to enter the home until firefighters arrived.
Once the fire was extinguished, they entered the home and discovered three people dead with fatal stab wounds, including a 12-year-old boy, 44-year-old woman, and a 30-year-old man.
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A 61-year-old woman, who suffered multiple stab wounds, was taken to a hospital in critical condition.
The two NYPD officers slashed were taken to a hospital with non-life-threatening injuries.
During a press conference after the incident, officials say Gordon, who has one prior arrest for strangulation in a domestic violence incident, is believed to have been visiting family at the residence.
The investigation is ongoing, as officials try to determine what led to Sunday's violent encounter.