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

Use m = 5, n = 9 and (x1,y1) = (3,2), (x2,y2) = (16,21).

x = 3 + (5/14)(16−3) = 3 + (5/14)(13) = 7.642857… ≈ 7.6
y = 2 + (5/14)(21−2) = 2 + (5/14)(19) = 8.785714… ≈ 8.8

So the treasure is at (7.6, 8.8).