L.A. does have Cartesian axes in practice, even if they aren’t really acknowledged. Broadway and 1st Street is origin. Addresses are numbered from here. The y-axis is Broadway, and it runs all the way from Lincoln Heights to Carson. The x-axis is 1st Street, which extends from the unincorporated area of East L.A. to just east of Beverly Hills (although not quite continuously.)

Of note, once Broadway crosses the L.A River, it no longer serves as the y-axis—east and west is delineated first by Pasadena Avenue, and north of that, by Figueroa Street—oddly enough, this puts Northeast L.A. in the northwest quadrant of L.A. Also, west of Beverly Hills, Sunset Boulevard serves as the x-axis from which addresses are numbered. San Pedro has its own Cartesian axes, implemented before it was annexed by L.A.

Using address numbering alone, it doesn’t make much sense to consider areas west of origin to be the Eastside (although there is that quirk with Northeast L.A. that I mentioned above.)

But what seems to be the best geographic feature to delineate the Eastside is the L.A River. Everything east of the river is the Eastside. What separates Northeast L.A. from the true Eastside is the Arroyo Seco.