Let the coordinates of the treasure be (x,y).
Let [tex] d_{1} [/tex] = distance from the rock to the treasure.
Let [tex] d_{2} [/tex] = distance from the tree to the treasure.
[tex] d_{1} = \sqrt{(x\2 + (y-2)^2} [/tex]
[tex] d_{2} = \sqrt{(16-x)^2 + (21-y)^2} [/tex]
We want [tex] \frac{ d_{1} }{ d_{2} } [/tex] = 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)
