We have conducted a photometric study of late-type members of the TW Hydrae association ( TWA ) and measured the rotation periods for 16 stars in 12 systems . For TWA stars listed by Webb et al . and Sterzik et al . ( TWA 1 - 13 ; led by TW Hya = TWA 1 ) we find a median period of 4.7 d. However , for stars that we measured in the TWA 14 - 19 group identified by Zuckerman et al. , we find a median period of only 0.7 d. The period distributions of the two groups can not be reconciled at the 3- \sigma significance level . Using photometric arguments supported by the Hipparcos distance to HD 102458 ( = TWA 19A ) , we find that TWA 14 - 19 reside at an average distance of d \approx 90 pc , spatially at the near boundary of the Lower Centaurus-Crux ( LCC ) subgroup of the Ophiuchus-Scorpius-Centaurus OB-star association ( OSCA ) . Proper motions for HD 102458 , TWA 14 , 18 and 19B link these stars to the LCC subgroup . From Hertzsprung-Russell ( H-R ) diagram placement , we derive an age of \approx 17 Myr for the HD 102458 system that may be the representative age for the TWA 14 - 19 group . Merging various lines of evidence , we conclude that these stars form a spatially- and rotationally-distinct population of older pre-main sequence ( PMS ) stars , rather than being an extension of the TWA beyond those stars associated with TW Hya that have an age of \sim 10 Myr and reside at d \approx 55 pc . Instead , TWA 14 - 19 likely represent the population of low-mass stars still physically associated with the LCC subgroup .