Order, Family Court, Bronx County (Carol R. Sherman, J.), entered on or about July 25, 2011, which, after a hearing, found that respondent-appellant had sexually abused his oldest daughter, derivatively abused the other three subject children, and neglected all four subject children, unanimously affirmed, without costs.
A preponderance of the evidence supports the court’s determination that respondent had sexually abused his oldest daughter (see Family Ct Act §§ 1012 [e] [iii]; 1046 [b] [i]). The daughter’s sworn testimony at the fact-finding hearing is competent evidence of abuse (Matter of Danielle M., 151 AD2d 240, 243 [1st Dept 1989]), and the absence of physical injury or other corroboration does not require a different result (see Matter of Jonathan F., 294 AD2d 121 [1st Dept 2002]; Danielle M., 151 AD2d at 243). There is no basis to disturb Family Court’s credibility determinations (Matter of Shirley C.-M., 59 AD3d 360, 361 [1st Dept 2009]). Once petitioner established its prima facie case, the burden shifted to respondent to explain his conduct and rebut the evidence of his culpability, which he failed to do (see Matter of Elizabeth S. [Dona M.], 70 AD3d 453, 453-454 [1st Dept 2010]). Although the court did not state that it was drawing a negative inference from respondent’s failure to testify, it was entitled to do so (see Matter of Nicole H., 12 AD3d 182, 183 [1st Dept 2004]).
Family Court’s determination that respondent had derivatively abused the other children is also supported by a preponderance of the evidence (see Family Ct Act § 1046 [a] [i]). Indeed, respondent’s daughter testified that one of her brothers had witnessed the sexual abuse and that the other children were present in the apartment when the abuse took place (see Matter of Marino S., 100 NY2d 361, 374 [2003]; Matter of Brandon M. [Luis M.], 94 AD3d 520, 520-521 [1st Dept 2012]).
A preponderance of the evidence also supports Family Court’s *455finding that respondent had neglected the children by abusing cocaine (see Family Ct Act § 1012 [f] [i] [B]). An agency caseworker testified that respondent admitted that he had last used cocaine a month before the hearing and was “high” when he returned home, and that he was not in a treatment program. In addition, respondent’s daughter testified that on one occasion, respondent had used cocaine while she was in the car. This proof was sufficient to trigger the application of the presumption of neglect under Family Court Act § 1046 (a) (iii), which obviates the need to establish the children’s impairment or risk of impairment (see Matter of Keoni Daquan A. [Brandon W.— April A.], 91 AD3d 414, 415 [1st Dept 2012]; Matter of Nasiim W. [Keala M.], 88 AD3d 452, 453 [1st Dept 2011]). Respondent failed to rebut this prima facie evidence of neglect (id.). Concur — Gonzalez, EJ., Saxe, Catterson, Acosta and Gische, JJ.