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The answer is (0,3) and (4,4).

   Select two points so that the distance between them is equal to 2 sqrt(5).     
   (0,3), (-20,15), (12,7), (3,4), (1,-8), (0,3), (4,4), (-5,8), (-10,-12)     

   Going to use Pythagoras' Theorem     

   c²  =  a² + b²     

   (2 sqrt(5))²  =  a² + b²     

   (4 • 5)  =  a² + b²     

   20  =  a² + b²     

   I can't make any of the provided pairs work.     

   However, take note that (0,3) is listed twice.     

   Why?  Let's assume there’s a typo.  What if     

   the second one were (10,3) instead.  When    

   we choose (10,3) & (12,7) we find precisely     

   what we want, the hypotenuse as follows:     

              c²  =  (7 – 3)² + (12 – 10)²       

              c²  =  4² + 2²  =  16 + 4     

              c²  =  20     

              c    =  sqrt(20)  =  2 sqrt(5)     

   _.