Awaterfall in a park is located 6 miles east and 3 miles north of the visitors center. there is a picnic site 1 mile east and 2 miles north of the visitors center. how long is a trail that goes directly from the waterfall to the picnic site? a. 2.9 miles c. 3.7 miles b. 1.2 miles d. 5.1 miles

Hello there!

if we define the y-axis as north and the x-axis as east, then we could use vectors (x,y) to represent the locations, where the (0,0) point is the visitors center.

The waterfall is in 6 miles east and 3 miles north of the (0,0), then we could represent it as (6,3)

the picnic site is 1 mile east and 2 miles north of the (0,0) then we could represent it as (1,2)

now we want to calculate the distance between these two points, first, we need to calculate the difference; this is:

(6,3) -(1,2) = (6 -1, 3-2) = (5,1)

if we want to calculate the total magnitude ( which is the total distance) of this vector, we need to use the Pythagorean theorem, where we considere the values of x and y as the cathetus of a triangle rectangle, and we want to obtain the hipotenuse of such triangle:

that we could round up to 5.1 miles, then the correct answer is the d.