What kind of correspondence there is between the points in the coordinate plane?

Answer 1

There are infinitely many possible correspondences between points in the coordinate plane.

Some examples:

Every point with coordinates (x+1, y) is one unit to the right of the point at (x, y).

Every point with coordinates (x, y+1) is one unit up from the point at (x, y). Every point with coordinates (x, -y) is the reflection, in the y-axis of the point at (x, y).