the ship from the starting point and at what ange 2 miles south to reach place \( B \). 3 miles straight from \( B \) to the southwest corner, reach \( C \). After that, 1 mile to the west Susu reached place D. How far and where is D from \( A \) ?

To solve this problem, we can use the concept of vectors and the addition of vectors to find the position of point D relative to point A. Let's denote the starting point as A, the point 2 miles south as B, the southwest corner as C, and the final point as D. We can represent the vectors as follows: - Vector AB: 2 miles south - Vector BC: 3 miles southwest - Vector CD: 1 mile west To find the position of point D relative to point A, we need to add the vectors AB, BC, and CD. Let's calculate the components of each vector: - Vector AB: 2 miles south, so the components are (0, -2) - Vector BC: 3 miles southwest, so the components are (-3, -3) - Vector CD: 1 mile west, so the components are (-1, 0) Now, we can add the vectors AB, BC, and CD to find the position of point D relative to point A: \[ \text{Vector AD} = \text{Vector AB} + \text{Vector BC} + \text{Vector CD} \] Let's calculate the components of Vector AD: \[ \text{Vector AD} = (0 + (-3) + (-1), -2 + (-3) + 0) \] \[ \text{Vector AD} = (-4, -5) \] Therefore, point D is 4 miles west and 5 miles south of point A.