Final answer:
The four properties that are distorted in map projections are size, shape, distance, and direction, with the Mercator projection notably distorting size as latitude increases.
Step-by-step explanation:
The four main properties that are distorted in different map projections are size (also known as area or scale), shape, distance, and direction. Each map projection distorts one or more of these properties in different ways to represent the three-dimensional Earth on a two-dimensional plane. For example, the Mercator projection keeps the shape of countries largely intact but distorts their size, especially as you move away from the equator. This leads to a visual misrepresentation where areas like Greenland appear much larger than they are in reality. Such distortions are inherent in the process of map-making and choosing a projection often involves a trade-off between preserving different properties.