Place an identical but scaled down map over the big original.
Is there a point where the same place on both maps coincide?
You can move and rotate (and scale) the small map...
Can you position the small map so that the answer to the above question would be affirmative?
Could there be more than one such point? Why ... ?
Choosing any positioning of the small map, is there a point where the same place on both maps coincide ?
Can you prove or disprove it?
Explore the applet by appropriate clicks... and think ...
Can you now answer the above questions?

You can simplify the problem by thinking about regular 'x' and 'y' coordinates (longitude and latitude) on a square and its sized down copy.
Of course, square (square map) could be changed to rectangular...