Question

A treasure map says that a treasure is buried so that it partitions the distance between a rock and a tree in a 5:9 ratio. Marina traced the map onto a coordinate plane to find the exact location of the treasure.

What are the coordinates of the treasure? If necessary, round the coordinates to the nearest tenth.

(11.4, 14.2)
(7.6, 8.8)
(5.7, 7.5)
(10.2, 12.6)

Answer 1

B

Explanation:

Answer 2

Let the coordinates of the treasure be (x,y).
Let
`d_(1)` = distance from the rock to the treasure.
Let
`d_(2)` = distance from the tree to the treasure.

`d_(1) = √((x\2 + (y-2)^2)`

`d_(2) = √((16-x)^2 + (21-y)^2)`
We want
`( d_(1) )/( d_(2) )` = 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)