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. x = (StartFraction m Over m + n EndFraction) (x 2 minus x 1) + x 1 y = (StartFraction m Over m + n EndFraction) (y 2 minus y 1) + y 1 What are the coordinates of the treasure? If necessary, round the coordinates to the nearest tenth.

Answer 1

b) (7.6, 8.8)

Explanation:

e 2020 ; )

Answer 2

A) (7.6, 8.8)

which are the coordinates of the treasure.

Missing Problem Statement:

Given Options:

A) (11.4, 14.2)

B) (7.6, 8.8)

C) (5.7, 7.5)

D) (10.2, 12.6)

I have added the picture showing the traced map onto a coordinate plane to find exact location of treasure.

The coordinates of Tree are (16,21)

Coordinates of rock are (3,2)

Explanation:

Let,

Coordinates of treasure be (a,b)

`d_(1)`= distance from tree to treasure

`d_(2)`=distance from rock to treasure

`d_(1)=√((16-x)^2 + (21-y)^2)`

`d_(2)=√(x\2 + (y-2)^2)`

Given ratio between rock and tree,
`(d_(2))/( d_(1))=(5)/(9)`= 0.55_______(Equation.1)

which will be used to locate the treasure.

Now we just need to cross check by putting the coordinates given in the options one by one to find out value of
`d_(1)`,
`d_(2)` and checking if it satisfies the Equation 1.

Check (A) (11.4, 14.2)

`d_(2)`= 14.8,
`d_(1)`= 8.2,

`(d_(2))/( d_(1))`= 1.8

Check (C) (5.7, 7.5)

`d_(2)`= 6.13,
`d_(1)`= 16.98,

`(d_(2))/( d_(1))`= 0.36

Check (D) (10.2, 12.6)

`d_(2)`= 12.8,
`d_(1)`= 10.2,

`(d_(2))/( d_(1))`= 1.25

Check (B) (7.6, 8.8)

`d_(2)`= 8.2,
`d_(1)`= 14.8,

`(d_(2))/( d_(1))`= 0.55

Which satisfies Equation 1, such that ratio between rock and tree is 5:9 or
`(d_(2))/( d_(1))=(5)/(9)`= 0.55

So, the coordinates of the treasure are (B) (7.6, 8.8)