You have coordinates of tree T(16,21) and of rock R(3,2). Let S be a point that denotes treasure. Since treasure is buried so that it partitions the distance between a rock and a tree in a 5:9 ratio, you can state that
[tex]\dfrac{\overrightarrow{RS}}{\overrightarrow{ST}}=\dfrac{5}{9}.[/tex]
Find the coordinates of these vectors:
[tex]\overrightarrow{RS}=(x_S-3,y_S-2), \\ \overrightarrow{ST}=(16-x_S,21-y_S).[/tex]
Then
[tex]\dfrac{x_S-3}{16-x_S} =\dfrac{5}{9}[/tex] and [tex]\dfrac{y_S-2}{21-y_S} =\dfrac{5}{9}.[/tex]
Solve these two equations:
1.
[tex]9(x_S-3)=5(16-x_S),\\ 9x_S-27=80-5x_S,\\ 9x_S+5x_S=80+27,\\14x_S=107,\\ \\x_S=\dfrac{107}{14}\approx 7.6.[/tex]
2.
[tex]9(y_S-2)=5(21-y_S),\\9y_S-18=105-5y_S,\\9y_S+5y_S=105+18,\\14y_S=123,\\ \\y_S=\dfrac{123}{14}\approx 8.8.[/tex]
Answer: the treasure are placed at point (7.6,8.8), so the correct choice is B.
