Question

Born in New York in 1856, Louise Blanchard Bethune is considered the first woman architect.

Answer 1

Born in New York in 1856, Louise Blanchard Bethune is considered the first woman architect.

"Born in New York in 1865" is a participial phrase.

Answer: A) PARTICIPIAL

Answer 2

If the underlined phrase is born in New York in 1856, then that would be a participial phrase, which often functions as an adjective in a sentence, like is the case here.
Gerund is always used as a noun, and infinitive has the form to + verb (to go, to be...)