To determine how far Andrew is from the starting point, we can use the concept of vector addition. Let's break down his movements step by step:
Andrew walks 10 km to the north. This movement takes him directly away from the starting point.
Andrew turns left and walks 4 km. This movement takes him to the west.
Andrew takes another left and continues walking 10 km forward. Since he turned left after walking 4 km to the west, this movement takes him to the south.
Now, let's analyze the total displacement in terms of north and west components:
North Component: Andrew initially walked 10 km to the north and then walked 10 km to the south, resulting in a net displacement of 10 km to the south.
West Component: Andrew walked 4 km to the west.
Now, we can calculate the magnitude of the total displacement using the Pythagorean theorem:
Total Displacement = √(North Component^2 + West Component^2) = √((10 km south)^2 + (4 km west)^2) = √(100 km^2 + 16 km^2) = √116 km^2 ≈ 10.77 km (rounded to two decimal places)
Therefore, Andrew is approximately 10.77 km away from the starting point. None of the given answer choices (A, B, C, D) exactly match this value, so none of the options provided are correct.