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
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.