Awomen starts at a point p on the earths surface and walks 1 mi south, then 1 mi east, then 1 mi north, and finds herself back at p, the starting point. describe all points p for which this is possible

Let point P be the center of the North pole. 

Any direction she moves 1 mi, she is walking 1 mi South.

1 mile is a very small distance but we can still think of the path as a little curved because of the shape of the Earth, but she is just moving in a straight path. 

Then the woman moves East, and then back North.

The linear equation is: y=ax+b