Which of the following is a valid property that all map projections exhibit?

All map projections exhibit some form of distortion in shape, area, distance, or direction because it is impossible to accurately represent the three-dimensional surface of the Earth on a two-dimensional plane without sacrificing some aspect of the representation. This inherent limitation arises from the need to translate the curvature of the Earth into a flat surface, necessitating compromises in the ways various properties are depicted.

For instance, when a globe, which accurately represents the Earth, is mapped onto a flat surface, certain features are distorted. Some projections may preserve the shape of landmasses but distort area, while others might maintain accurate distances but not shape. Therefore, every map projection will alter at least one of these properties, leading to the conclusion that distortion is inevitable in any map projection.

In contrast, complete accuracy of distance, no distortion at all, and maintenance of the actual physical surface of the Earth are not properties that can be universally met across all map projections. Each of these aspects would inherently lead to significant inaccuracies in the portrayal of the Earth's features when projected onto a flat surface.