  The scaling property of large-$p_\perp$ hadron suppression,
$R_{\rm{AA}}(p_\perp)$, measured in heavy ion collisions at RHIC and LHC leads
to the determination of the average parton energy loss $\langle \epsilon
\rangle$ in quark-gluon plasma produced in a variety of collision systems and
centrality classes. Relating $\langle \epsilon \rangle$ to the particle
multiplicity and collision geometry allows for probing the dependence of parton
energy loss on the path-length $L$. We find that $\langle \epsilon \rangle
\propto L^\beta$ with $\beta=1.02^{+0.09}_{-0.06}$, consistent with the pQCD
expectation of parton energy loss in a longitudinally expanding quark-gluon
plasma. We then demonstrate that the azimuthal anisotropy coefficient divided
by the collision eccentricity, $v_2/\textrm{e}$, follows the same scaling
property as $R_{\rm{AA}}$. This scaling is observed in data, which are
reproduced by the model at large $p_\perp$. Finally, a linear relationship
between $v_2/\textrm{e}$ and the logarithmic derivative of $R_{\rm{AA}}$ is
found and confirmed in data, offering an additional way to probe the $L$
dependence of parton energy loss using coming measurements from LHC Run 3.
