ABSTRACT This paper presents an alternative way of analysing baryon acoustic oscillation (BAO) distance measurements via rotations to define new quantities ${\cal D}^{\rm perp}$ and ${\cal D}^{\rm par}$. These quantities allow simple tests of consistency with the Planck $\Lambda$cold dark matter (Λ CDM) cosmology.1 The parameter ${\cal D}^{\rm perp}$ is determined with negligible uncertainty from Planck under the assumption of $\Lambda$CDM. Comparing with measurements from the Dark Energy Spectroscopic Instrument (DESI), we find that the measurements of ${\cal D}^{\rm perp}$ from Data Release 2 (DR2) move into significantly better agreement with the Planck $\Lambda$CDM cosmology compared to DESI Data Release 1 (DR1). The quantity in the orthogonal direction ${\cal D}^{\rm par}$ provides a measure of the physical matter density in the $\Lambda$CDM cosmology. The DR2 measurements of ${\cal D}^{\rm par}$ remain consistent with Planck $\Lambda$CDM despite the substantial improvement in their accuracy compared to the earlier DR1 results. Comparing Planck and DESI BAO measurements, we find no significant evidence in support of evolving dark energy. We also investigate a rotation in the theory space of the $w_0$ and $w_a$ parametrization of the dark energy equation-of-state $w(z)$. We show that the combination of DESI BAO measurements and the CMB constrain $w(z=0.5) = -0.996 \pm 0.046$, very close to the value expected for a cosmological constant. We present a critique of the statistical methodology employed by the DESI collaboration and argue that it gives a misleading impression of the evidence in favour of evolving dark energy. An appendix shows that the cosmological parameters determined from the Dark Energy Survey 5 Year supernova sample are in tension with those from DESI DR2 and parameters determined by Planck.