For this question, we determine first the x and y components of the distances.
3 blocks north:
x - component = +3 ; y-component = 0
4 blocks northeast:
x - component = (cos 45°)(4 blocks) = 2.83 blocks
y - component = (cos 45°)(4 blocks) = 2.83 blocks
5 blocks west:
x-component = -5 ; y-component = 0
Then, we add up all the x-components and all the y-components
x-component (sum) = 0.83
y-component (sum) = 2.83
Then, we determine the magnitude of the block by the equation below.
m = √(x² + y²) = √(0.83² + 2.83²) ≈ 2.95 blocks
Thus, the displacement from the original position is approximately equal to 2.95 blocks.
