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.

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

Answer 1

Using proportions, it is found that the coordinates of the treasure as given as follows: (7.6, 8.8).

What is a proportion?

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

Researching the problem on the internet, the coordinates are as follows:

• Rock (3,2).

• Treasure (x,y).

• Tree (16,21).

The treasure is buried between a rock and a tree in a 5:9 ratio, hence the expression is:

$Ts - R = \frac{5}{14}(Tr - R)$

Hence, for the x-coordinate:

$x - 3 = \frac{5}{14}(16 - 3)$

x - 3 = 5 x 13/14

x = 7.6.

For the y-coordinate:

$y - 2 = \frac{5}{14}(21 - 2)$

y - 2 = 5 x 19/14

y = 8.8.

More can be learned about proportions at https://brainly.com/question/24372153

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