Let the coordinates of the treasure be (x,y).
Let 

 =  distance from the rock to the treasure.
Let 

 =  distance from the tree to the treasure. 


We want 

 = 5/9 in order to locate the treasure. 
Note that 5/9 = 0.556 (approx)
Test (11.4, 14.2)
d1 = 14.8, d2 = 8.2, d1/d2 = 1.8           Incorrect
Test (7.6, 8.8)
d1 = 8.2,  d2 = 14.8,  d1/d2 = 0.554    Correct
Test (5.7, 7.5)
d1 = 6.13,  d2 = 16.98,  d1/d2 = 0.36   Incorrect
Test (10.2, 12.6)
d1 = 12.8,  d2 = 10.2,  d1/d2 = 1.255   Incorrect
Answer: 
The correct answer is (7.6, 8.8)