They figure that the waterfall is at point (3,6). The overlook is at point (0,1). The campsite is at point (3,-5). The lake is point (-4,1). And the parking lot is at point (0,-5). Which of these pairs of locations are closest to one another?
The distance between two points (x1, y1) and (x2, y2) can be calculated using the distance formula:
Distance = sqrt((x2-x1)^2 + (y2-y1)^2)
Calculating the distances between the given points:
1. Distance between waterfall (3,6) and overlook (0,1):
Distance = sqrt((0-3)^2 + (1-6)^2) = sqrt(9 + 25) = sqrt(34) ≈ 5.83
2. Distance between waterfall (3,6) and campsite (3,-5):
Distance = sqrt((3-3)^2 + (-5-6)^2) = sqrt(0 + 121) = sqrt(121) = 11
3. Distance between waterfall (3,6) and lake (-4,1):
Distance = sqrt((-4-3)^2 + (1-6)^2) = sqrt(49 + 25) = sqrt(74) ≈ 8.60
4. Distance between waterfall (3,6) and parking lot (0,-5):
Distance = sqrt((0-3)^2 + (-5-6)^2) = sqrt(9 + 121) = sqrt(130) ≈ 11.40
Therefore, the pair of locations that are closest to one another is the waterfall (3,6) and the overlook (0,1).