Instructions: Amit was driving in New Town, where all roads run either north-south or east-west, forming a grid. Roads are at a distance of 1 km from each other and are parallel.
After driving as stated in the previous question (3 km north, 3 km west, then 4 km south from his starting point), Amit did not return to his starting point but instead drove a further 4 km east and 1 km north. How far is he from his starting point?
Show Hint
After the extra move the north-south offset cancels to zero, leaving only a 1 km east-west gap.
Tracking the east-west and north-south balances directly, without full coordinates, gives the same answer more quickly.
Before this last move, the balances were: north-south $=-1$ (1 km south of start), east-west $=-3$ (3 km west of start).
The extra move adds $+4$ to east-west and $+1$ to north-south.
New east-west balance: $-3+4=+1$, meaning 1 km east of the start line.
New north-south balance: $-1+1=0$, meaning exactly level with the start line, no north-south offset left.
With a 0 km north-south offset and a 1 km east offset, the straight-line distance from the start is simply $1$ km, since one of the two components is zero.
