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.


Answer: 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.