what distance formula would you use to solve this problem? A boat starts at point A, moves 3 km due north, then 2km due east, then 1 km due south, and 4km due east to point B. Find the distance AB.

perform the movement on a grid, I have it ending up at B (6,2) from A(0,0)

AB = √( (6-0)^2 + (2-0)^2 ) = √40 or 2√10

To find the distance AB, we can use the Pythagorean theorem. The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, we can consider the movement along the north as the vertical side (let's call it side 'a') and the movement along the east as the horizontal side (let's call it side 'b') of the right triangle.

So, the distance AB can be found using the formula: distance AB = √(a^2 + b^2).

Let's calculate the distance AB step by step:

1. First, let's calculate the vertical side (side 'a') of the triangle. The boat moves 3 km due north, so the length of side 'a' is 3 km.

2. Next, let's calculate the horizontal side (side 'b') of the triangle. The boat moves 2 km due east, then 4 km due east, so the total displacement in the eastward direction is 2 km + 4 km = 6 km. Therefore, the length of side 'b' is 6 km.

3. Now, we can substitute the values of 'a' and 'b' into the formula to find the distance AB:
distance AB = √(3^2 + 6^2) = √(9 + 36) = √45 = 6.71 km (approximate to two decimal places).

Therefore, the distance AB is approximately 6.71 km.