the water fall is at point (3, 6) the overlook is at point (0, 1) the campsite is at point (3, -5) the lake is at point (-4, 1) and the parking lot is at point (0, -5) whic of these parirs of locations are closest from one another

Answer 1

To determine which pairs of locations are closest to one another, we can calculate the distances between each pair of points. Let's calculate the distances for each pair:

1) Distance between the waterfall (3, 6) and the overlook (0, 1):
Distance = √[(3 - 0)^2 + (6 - 1)^2] = √(3^2 + 5^2) = √(9 + 25) = √34 ≈ 5.83

2) Distance between the waterfall (3, 6) and the campsite (3, -5):
Distance = √[(3 - 3)^2 + (6 - (-5))^2] = √(0^2 + 11^2) = √(0 + 121) = √121 = 11

3) Distance between the waterfall (3, 6) and the lake (-4, 1):
Distance = √[(3 - (-4))^2 + (6 - 1)^2] = √(7^2 + 5^2) = √(49 + 25) = √74 ≈ 8.60

4) Distance between the waterfall (3, 6) and the parking lot (0, -5):
Distance = √[(3 - 0)^2 + (6 - (-5))^2] = √(3^2 + 11^2) = √(9 + 121) = √130 ≈ 11.40

5) Distance between the overlook (0, 1) and the campsite (3, -5):
Distance = √[(0 - 3)^2 + (1 - (-5))^2] = √((-3)^2 + 6^2) = √(9 + 36) = √45 ≈ 6.71

6) Distance between the overlook (0, 1) and the lake (-4, 1):
Distance = √[(0 - (-4))^2 + (1 - 1)^2] = √(4^2 + 0^2) = √16 = 4

7) Distance between the overlook (0, 1) and the parking lot (0, -5):
Distance = √[(0 - 0)^2 + (1 - (-5))^2] = √(0^2 + 6^2) = √36 = 6

8) Distance between the campsite (3, -5) and the lake (-4, 1):
Distance = √[(3 - (-4))^2 + (-5 - 1)^2] = √(7^2 + (-6)^2) = √(49 + 36) = √85 ≈ 9.22

9) Distance between the campsite (3, -5) and the parking lot (0, -5):
Distance = √[(3 - 0)^2 + (-5 - (-5))^2] = √(3^2 + 0^2) = √9 = 3

10) Distance between the lake (-4, 1) and the parking lot (0, -5):
Distance = √[(-4 - 0)^2 + (1 - (-5))^2] = √((-4)^2 + 6^2) = √(16 + 36) = √52 ≈ 7.21

From the calculations, we can determine that the pairs of locations closest to one another are:

1) The overlook (0, 1) and the lake (-4, 1) with a distance of 4.
2) The campsite (3, -5) and the parking lot (0, -5) with a distance of 3.