Last passage percolation is a model of random planar geometry which captures notions of distances and geodesics. It admits a rich scaling limit, called the directed landscape, that is conjectured to be universal for all geometric models in the so called KPZ universality class. A closely related notion is the KPZ fixed point, which represents the scaling limit of certain growing interfaces. A variational formula links the evolution of the KPZ fixed point to the directed landscape. The optimizer of the variational formula is akin to the polymer endpoint of a point-to-line last passage percolation problem. I will explain how to compute the law of this endpoint using the integrability of the KPZ fixed point. Joint work with Jeremy Quastel and Sourav Sarkar.