Answer: 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.