Orient the page first
North up, South down, East right, West left. Every turn is relative to the direction the person currently faces, so track their facing at each step.
Facing North and turning right => now facing East.
Rapid Revision · Logical Reasoning
Direction Sense
Track a person turning left and right across a grid and find their final direction or distance from the start. Draw it and use Pythagoras.
The 3-minute recap
If you read nothing else tonight, read these 5 lines.
- Set North up and East right on your page, and draw every move to rough scale.
- A right turn rotates you 90 degrees clockwise; a left turn 90 degrees anticlockwise.
- Shortest (straight-line) distance from the start = sqrt(x^2 + y^2).
- At sunrise the shadow falls WEST; at sunset it falls EAST (shadow opposite the sun).
- Net displacement, not total path walked, is what 'how far from start' asks for.
Formula sheet
Every formula for direction sense in one place, each labelled so you know exactly when to reach for it. Screenshot it the night before.
Straight-line distance
distance = sqrt(x^2 + y^2)
x = net East-West, y = net North-South displacement.
Right turn
rotate facing 90 degrees clockwise: N -> E -> S -> W -> N
Left turn
rotate facing 90 degrees anticlockwise: N -> W -> S -> E -> N
Shadows
morning: shadow to WEST evening: shadow to EAST
Work through the cards
6 cards, each one idea: what it is, a worked example, and the trap to dodge.
Turns are relative
Left and right depend on current facing, not the page. Redraw the facing arrow after each turn before moving on.
Trap: Turning right while facing South points you WEST, not East. Always rotate from the current facing.
Net displacement with coordinates
Put the start at (0,0). East and West change x, North and South change y. Sum the moves; the final (x, y) is the displacement.
5 East then 3 West nets +2 on x; the straight distance ignores the doubling back.
Straight-line distance
With net x and net y, the direct distance is sqrt(x^2 + y^2). Right-angled paths make this a clean one-step Pythagoras.
3 North then 4 East => distance = sqrt(9 + 16) = 5.
Shadows and the sun
Morning sun is in the East, so shadows point West; evening sun is West, so shadows point East. At noon shadows are negligible.
Trap: The shadow always falls opposite the sun. Get this backwards and every sub-answer flips.
Final facing direction
If the question asks which direction the person now faces, track only the turns, the distances do not matter for facing.
Go deeper
A recap is not practice. These are the creators we rate for real depth on direction sense; full credit to each.
One topic down. Keep the streak going.
Each recap takes 3 minutes; the full set covers everything the first round tests. And when the test is cleared, your resume takes the next screen.
Original content by OptiResume; facts and formulas are common knowledge, the wording is ours. Go-deeper links go to creators we rate; we are not affiliated with them.