NEW YORK (AP) — U.S. Supreme Court Justice Sonia Sotomayor returned Friday to the Bronx housing project where she spent part of her childhood, recalling how an unlikely encounter there with Robert F. Kennedy ignited her passion for public service.

The Bronx native fought back tears at the ceremony renaming the Bronxdale Houses after Sotomayor.

In an emotional speech, Sotomayor said she lived in the project during the most formative years of her life. On a spring afternoon in 1958, she looked out of her second-story window and saw a famous face.

‘‘Robert Kennedy was coming to visit our projects. I had never before looked down on red hair that bright,’’ she said, adding that she went to the library to look him up.

‘‘I was captivated by his career. Through this chance encounter above the old community center, my interest in public service was awakened.’’

With many residents of the complex listening in the audience, and her mother wiping away tears in the front row, Sotomayor reflected on a childhood that was spent surrounded by family. Her cousins, also from the projects, would join her at the local fast food joint for hamburger-eating competitions, she said.

‘‘I do remember each time I drive by that White Castle, the hours and hours of laughter that my cousins and I had as we roamed the grounds of this housing project, and played in the playgrounds, and screamed and fought and laughed and lived,’’ she said.

The scene at the ceremony Friday was a far cry from the anonymous existence Sotomayor had once known there. Mayor Michael Bloomberg introduced her, and Sen. Charles Schumer stopped by to pay his respects.

After speaking, she danced on stage with the choir from her alma mater, Cardinal Spellman High School.

Darryl Moore, a 42-year-old resident walking nearby with his 4-year-old daughter, said he hoped the new name — the Justice Sonia Sotomayor Houses and Community Center — would be a reminder to his children that they could go far in life no matter where they grew up.

‘‘It’s good to know somebody that came from housing and went on to be successful. Hopefully with her name here some better things will happen,’’ he said.

But other community members questioned why the development was honoring someone who they said seemed disconnected from the community.

‘‘They shouldn’t change the name,’’ said 21-year-old Mikayla Workman, a former resident who was back visiting her boyfriend and grandmother. ‘‘She hasn’t done nothing. There’s still rat holes. People still complain about paint chipping.’’

Regina Howell, the president of the complex’s tenants association, said most tenants who responded to a door-to-door survey supported the name change.

Sotomayor also visited her nearby elementary school, Blessed Sacrament, where children cheered excitedly as the justice entered an assembly to present an award to student David Abreu.

‘‘I think I have a lot more responsibility now,’’ said the beaming and genuinely surprised seventh-grader.

Sotomayor assured the children that she was once a kid just like them. In those days, she aspired to be a lawyer, but never dreamed she’d get to the Supreme Court.

Later in the day, Sotomayor said in a commencement address at Hostos Community College that the school’s opening in 1970 created an opportunity for her mother, Celina Baez, to pursue an education ‘‘and it opened the path to where I am today.’’

‘‘Finally there was an institution that offered the right mix of educational and support services to give my mom a chance to attain her aspirations of becoming a nurse,’’ Sotomayor said, adding that her mother’s return to school at the age of 47 gave her children a powerful example.

The school’s current president, Felix Matos Rodriguez, said Sotomayor’s success is an example of how community colleges can create social mobility for students.

‘‘They get their chance to realize their potential and to transform their lives and the lives of their children,’’ Matos Rodriguez said.

Hostos was founded in 1968 as part of the City University of New York amid a clamor for an educational institution to meet the needs of Spanish-speaking residents.

A first class of 623 entered in the fall of 1970. This year, it had a spring enrollment of over 6,000 students, and the bilingual school continues to embrace its role as a gateway to higher education for Latin American immigrants.

Of the 334 students who expected to receive degrees Friday, most are Hispanic or black and nearly 35 percent are graduates of foreign high schools.

Melissa Diaz, 26, the school’s valedictorian, said her life was echoed in Sotomayor’s story. Her mother also attended Hostos. Like Sotomayor, who studied at Princeton University and is of Puerto Rican background, Diaz has been accepted to an Ivy League school.

‘‘This college is very strong and nurturing,’’ said Diaz, who is of Puerto Rican and Dominican descent.