Concept 3 of 4
Position Tracker: Follow the Path
Today's big idea
Sketch every leg, because each turn changes which way the next walk goes.
Each leg moves you the way you now face, so track the net north-south and east-west.
How it works
👀 What's going on?
A tracking question hands you a chain of walks and turns and asks where you finish. Doing it in your head nearly always goes wrong. Drawing it nearly never does.
💡 Here's the trick
Look at the path above. Starting north, walk 4 m, then turn right to face east and walk 3 m. That leaves you 4 m north and 3 m east of the start, which is north-east. Every turn changes the direction you face, and every walk moves you whichever way you face now.
🪄 How to do it
- 1.Mark your starting dot and facing, as the picture above starts facing north.
- 2.Draw each walk as an arrow, updating your facing at every turn.
- 3.Read the finish as so far north or south, and so far east or west.
✍️ Try it
Face East and walk 5 m. Turn 90° right and walk 2 m. Turn 90° right again and walk 5 m. Where do you finish?
The two 5 m legs cancel, because the first heads east and the third heads west. That leaves only the middle leg, so you finish 2 m due south of where you began. Sketching it shows the cancellation straight away.
⚠️ Watch out
You might be thinking a right turn always points you east. Right depends entirely on which way you already face. Facing east, a right turn takes you south, and facing south it takes you west.
🌟 Why this matters
Following directions through a building, retracing your steps to find something dropped, or planning a route round a park all work like this. Sketching as you go stops a chain of turns becoming a muddle.
Exam tip: Draw the arrows even for short walks, because the mistakes come from the turns rather than the distances.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“Face W. Walk 5 m. Turn left. Walk 2 m. Direction from start?”
- 1
Step 1
5 m West.
- 2
Step 2
Turn left → now facing South. Walk 2 m south.
- 3
Position
5 m West + 2 m South of start.
- 4
Answer ✓
End is South-West of start
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Walk the path: 3 West, then 4 North.
PATH · ROUND 1 OF 3
↑ N
Quick check
✅ VERIFICATION
Face North and walk 3 m. Turn 90° left and walk 4 m. Where are you from the start?
⚡ Finish the activity above first to answer.
Keep going!
Up next: Calendar Walker
7 = same day. Walk only the leftover.