Explain two different ways that two-dimensional people in Flatland use to distinguish their positions (North and South).
Because Flatland is two-dimensional, the people living there have only a sense of cardinal directions, but because the land is very same-looking all over, and because of the fog, it is hard to tell which direction is which. The natural laws of the land account for this, however, and help in two distinct ways. First, all living things in Flatland have a natural inclination to the South, as if pulled by an invisible force:
There being no sun nor other heavenly bodies, it is impossible for us to determine the North in the usual way; but we have a method of our own. By a Law of Nature with us, there is a constant attraction to the South... the hampering effect of the southward attraction is quite sufficient to serve as a compass in most parts of our earth.
(Abbot, Flatland, geom.uiuc.edu)
This attraction allows the people of Flatland to distinguish North and South, and by association East and West, making navigation easier.
The other way is based on climate and environment; rain, which does not fall "down" but instead flows South from the North at regular times. This allows the people to build in ways to keep rainflow out of their houses, as well as affecting the "trees" and other natural landscape objects in some undefined way. The narrator relates a story from his own life in which he was forced to stay still in a temperate, uninhabited area where the natural Southern attraction was weaker; when the rain flowed to the South, he was able to figure out his directions and continue his journey.