Question

On a coordinate plane, a line is drawn from Rock to Tree. The x- and y-axes are labeled feet. Rock is at (3, 2) and Tree is at (16, 21).

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

(7,6, 8,8)

Explanation:

Answer 2

The second choice
`(7.6,8.8)`

Explanation:

The missing image is attached

We use the section formula:

`(x,y)=((mx_2+nx_1)/(m+n),(my_2+ny_1)/(m+n))`

We substitute
`x_1=3,x_2=16,y_1=2,y_2=21` and m=5, n=9

`(x,y)=((5*16+9*3)/(5+9),(5*21+5*2)/(9+5))`

We simplify to get:

`(x,y)=((80+27)/(14),(105+10)/(14))`

This simplifies to:

`(x,y)=((107)/(14),(125)/(14))`

In decimals we get:

`(x,y)=(7.6,8.8)`