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.

A. (11.4, 14.2)
B. (7.6, 8.8)
C. (5.7, 7.5)
D. (10.2, 12.6)

Answer 1

Option B. is the answer.

Explanation:

The given question is incomplete without the attachment; here is the attachment enclosed with the answer.

Since coordinates of the point representing rock is (3, 2) and coordinates of the tree are (16, 21) and treasure divides the line joining rock and tree in the ratio of 5:9.

We know the formula to get the coordinates of point P(x, y) joining (a, b) and (c, d) in the ratio of m : n is

P(x, y) =
`[((mc+na))/(m+n), ((md+nb))/(m+n)]`

From the given formula,

Coordinates of treasure P =
`[(((5* 16)+(9* 3))/((5+9)), ((5* 21)+(9* 2))/((5+9))]`

=
`[((80)+(27))/((14)), ((105)+(18))/((14))]`

=
`[7.64, 8.78]`

≈ (7.6, 8.8)

Therefore, Option B will be the answer.