  When the value $L$ of the directed landscape at a point
$(\mathbf{p};\mathbf{q})$ is sufficiently large, the geodesic from $\mathbf{p}$
to $\mathbf{q}$ is rigid and its location fluctuates of order $L^{-1/4}$ around
its expectation. We further show that at a midpoint of the geodesic, the
location of the geodesic and the value of the directed landscape after
appropriate scaling converge to two independent Gaussians.
