The SF1 DNA helicases are multi-domain proteins that can unwind duplex DNA in reactions that are coupled to ATP binding and hydrolysis. Crystal structures of two such helicases, Escherichia coli Rep and Bacillus stearothermophilus PcrA, show that the 2B sub-domain of these proteins can be found in dramatically different orientations (closed versus open) with respect to the remainder of the protein, suggesting that the 2B domain is highly flexible. By systematically using fluorescence resonance energy transfer at the single-molecule level, we have determined both the orientation of an E.coli Rep monomer bound to a 3'-single-stranded-double-stranded (ss/ds) DNA junction in solution, as well as the relative orientation of its 2B sub-domain. To accomplish this, we developed a highly efficient procedure for site-specific fluorescence labeling of Rep and a bio-friendly immobilization scheme, which preserves its activities. Both ensemble and single-molecule experiments were carried out, although the single-molecule experiments proved to be essential here in providing quantitative distance information that could not be obtained by steady-state ensemble measurements. Using distance-constrained triangulation procedures we demonstrate that in solution the 2B sub-domain of a Rep monomer is primarily in the "closed" conformation when bound to a 3'-ss/ds DNA, similar to the orientation observed in the complex of PcrA bound to a 3'-ss/ds DNA. Previous biochemical studies have shown that a Rep monomer bound to such a 3'-ss/ds DNA substrate is unable to unwind the DNA and that a Rep oligomer is required for helicase activity. Therefore, the closed form of Rep bound to a partial duplex DNA appears to be an inhibited form of the enzyme.