Concept 3 of 5
Path Walking: Where Did You End Up?
Today's big idea
Only the finish counts, so draw each leg and compare the end against the start.
Legs pointing opposite ways cancel, so distance walked is not distance moved.
How it works
👀 What's going on?
You leave home, walk a few blocks one way, then a few another way. Someone asks which direction you are from home now. Holding the whole journey in your head at once is what makes this hard.
💡 Here's the trick
Look at the walk above. Each leg is drawn one at a time from a dot marking home, and only the finishing dot matters. Going up and right lands you north-east of home, and going down and left lands you south-west. Legs that point opposite ways cancel each other out.
🪄 How to do it
- 1.Mark home as a dot, the way the walk above starts.
- 2.Draw each leg in turn, east to the right, north upwards.
- 3.Compare only the finish with the dot you started from.
✍️ Try it
Walk 4 blocks South, then 6 blocks East. Then try: walk 2 blocks West, then 5 blocks North, then 2 blocks East.
The first walk finishes below home and to its right, which is South-East. In the second, the 2 west and the 2 east cancel, leaving only the 5 north, so you end up due North of home.
⚠️ Watch out
You might be thinking every leg you walk shows up in the answer. Walk 3 blocks north and then 3 blocks south and you are standing exactly where you began. Opposite legs cancel, and the answer is where you stopped, not how far you went.
🌟 Why this matters
Working out where you have ended up relative to where you set off is what you do leaving a station or a shopping centre. Only the start and the finish decide it.
Exam tip: Draw the dot and the legs rather than reasoning in your head, since one missed leg changes the answer.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“Start at home. Walk 3 blocks East, then 2 blocks North. Where are you compared to home?”
- 1
Draw the start
Mark home with a dot. 🏠
- 2
Walk 3 blocks East
Move 3 squares right.
- 3
Walk 2 blocks North
Now move 2 squares up from there.
- 4
Read end vs start
End is RIGHT of home AND ABOVE home. That's North-East.
- 5
Answer ✓
End is North-East of home
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Walk the path: 3 East, then 2 North.
PATH · ROUND 1 OF 3
↑ N
Quick check
✅ VERIFICATION
You walk 3 blocks North and then 3 blocks South. Where are you now?
⚡ Finish the activity above first to answer.
Keep going!
Up next: Turn-Around
Right = clockwise. Left = other way. 180° = opposite.