A boat starts at point A, moves 3 km due north, then 2 km die east, then 1 km due south, and then 4 km die east to point B. Find the distance AB.
North 3 - 1 = 2
east 2 + 4 = 6
distance = sqrt (2^2 + 6^2) = sqrt(40) = 2 sqrt(10)
47, cuz I said so
To find the distance between points A and B, we can use the Pythagorean theorem. Let's break down the boat's movement step by step:
1. The boat moves 3 km due north from point A. This adds 3 km to the boat's latitude position.
2. Next, the boat moves 2 km due east from its new position. This adds 2 km to the boat's longitude position.
3. Then, the boat moves 1 km due south. This subtracts 1 km from the boat's latitude position.
4. Finally, the boat moves 4 km due east from its new position. This adds 4 km to the boat's longitude position.
Now, let's calculate the latitude and longitude coordinates of point B:
Latitude: 3 km north - 1 km south = 2 km north
Longitude: 2 km east + 4 km east = 6 km east
Using the Pythagorean theorem, which states that the square of the hypotenuse (AB) of a right triangle is equal to the sum of the squares of the other two sides, we can find the distance between A and B:
Distance AB = √(latitude^2 + longitude^2)
= √(2 km^2 + 6 km^2)
= √(4 km^2 + 36 km^2)
= √(40 km^2)
= 2√10 km
Therefore, the distance between points A and B is 2√10 km.