Topological semimetals with nontrivial band crossing points have attracted widespread interest in recent years. Here, we propose that AB₂ (A = Cr, Mo; B = Si, Ge) compounds are topological semimetals that feature a pair of triple points (TPs) on high-symmetry paths in the absence of spin–orbital coupling (SOC). In particular, the existence of this kind of TP is accompanied by a quadratic nodal line (QNL). In addition, we discover that these TPs are movable. Under a triaxial strain, we can change their positions on high-symmetry paths. When considering SOC, TPs transform into two pairs of type-II Dirac points along the high-symmetry path. Akin to TPs without SOC, each pair of Dirac points can also shift their positions on the high-symmetry paths under a triaxial strain. To characterize this property of TPs and Dirac points, we construct an effective model around the TPs and Dirac points, finding that there indeed exists a parameter that could characterize the movable properties for the TPs and Dirac points. According to the bulk-surface correspondence, we also discover that the length of the Fermi arcs that correspond to the nontrivial band crossings are also altered when changing their positions. Meanwhile, the shapes of Fermi arcs are also changed. Therefore, our work provides a platform to study the band crossings that are movable. The controllable fermions are beneficial to utilize the topological materials in nano-devices.