Say that you take 1 step left, then 2 forward, then 4 right, then 3 right, then 3 forward, then 5 back. Take me through the process of determining how far you end up from your starting position.


First, we find the displacement from the starting position, which we will use to calculate the distance. To do this, collect the steps into groups by direction.

Left: we take 1 step left
Right: we take 4 + 3 = 7 steps right
Forward: we take 2 + 3 = 5 steps forward
Back: we take 5 steps back

We can subtract step counts in opposite directions to get our final displacement

Left/Right: we take 1 step left and 7 right, so we take a total of 1 - 7 = -6 steps left. This is equivalent to 6 steps right.
Forward/Back: we take 5 steps forward and 5 steps back, so we take a total of 5 - 5 = 0 steps forward.

This means we end up 5 steps to the right and 0 steps forward from where we started, which is a distance of 5 steps.