Although the crystal structures of the copper oxide high-temperature superconductors are complex and diverse, they all contain some crystal planes consisting of only copper and oxygen atoms in a square lattice: superconductivity is believed to originate from strongly interacting electrons in these CuO2 planes. Substituting a single impurity atom for a copper atom strongly perturbs the surrounding electronic environment and can therefore be used to probe high-temperature superconductivity at the atomic scale. This has provided the motivation for several experimental and theoretical studies. Scanning tunnelling microscopy (STM) is an ideal technique for the study of such effects at the atomic scale, as it has been used very successfully to probe individual impurity atoms in several other systems. Here we use STM to investigate the effects of individual zinc impurity atoms in the high-temperature superconductor Bi2Sr2CaCu 2O8+δ. We find intense quasiparticle scattering resonances at the Zn sites, coincident with strong suppression of superconductivity within ~15 Å of the scattering sites. Imaging of the spatial dependence of the quasiparticle density of states in the vicinity of the impurity atoms reveals the long-sought four-fold symmetric quasiparticle `cloud' aligned with the nodes of the d-wave superconducting gap which is believed to characterize superconductivity in these materials.