Internet coordinate-based systems are poised to become an important service to support overlay construction and topology-aware applications. Indeed, through network distance embedding into an appropriate geometric space, such systems allow for accurate network distance estimations with low overhead. However, coordinate systems often rely on good cooperation between nodes for correct coordination and assume that information reported by probed nodes is correct. In this paper, we identify various attacks against coordinate embedding systems and show their effectiveness on two representative positioning systems, namely Vivaldi and NPS. Our study demonstrates that these attacks can seriously disrupt the operations of these systems and therefore the virtual networks and applications relying on them for distance measurements. Through simulations of different potential scenarios where malicious nodes provide biased coordinate information and delay measurement probes, we quantify the effects of attack strategies that aim to (i) introduce disorder in the system, (ii) fool honest nodes to move far away from their correct positions and (iii) isolate particular target nodes in the system through collusion. Our findings confirm the susceptibility of the coordinate systems to such attacks.