8.20 Quick Revision -- Direction Sense

The Compass (Draw This First -- Always!)

            N
            |
   NW ------+------ NE
            |
   W -------+------- E
            |
   SW ------+------ SE
            |
            S

Turn Rules

From	Right (CW 90)	Left (ACW 90)	About Turn (180)
N	E	W	S
E	S	N	W
S	W	E	N
W	N	S	E

Clockwise: N -> E -> S -> W -> N

Shadow Rules

Time	Sun	Shadow	Shadow Left	Shadow Right	Shadow Front	Shadow Behind
Morning	East	West	Face N	Face S	Face W	Face E
Evening	West	East	Face S	Face N	Face E	Face W
Noon	Overhead	None/minimal	--	--	--	--

Shortest Distance Formula

  Shortest Distance = sqrt(X_net^2 + Y_net^2)

Where X_net = total East - total West, Y_net = total North - total South.

Key Pythagorean Triplets

  3, 4, 5  |  5, 12, 13  |  6, 8, 10  |  8, 15, 17  |  7, 24, 25

Coordinate Approach (for 3+ turns)

• Start at (0, 0)
• North = +Y, South = -Y, East = +X, West = -X
• NE = (+d/sqrt(2), +d/sqrt(2)), etc.

Common Traps

1. "Direction of A FROM B" = Stand at B, look toward A
2. Left/Right are RELATIVE to facing; N/S/E/W are ABSOLUTE
3. Walking NE for d km gives d/sqrt(2) in each component
4. Net turn = sum of all CW turns (positive) and ACW turns (negative)

Exam Strategy

• Simple (2-3 turns): Solve mentally, ~30 sec
• Medium (4-5 turns): Quick sketch, ~60 sec
• Complex (6+ turns): Coordinate method, ~90 sec
• Shadow problems: Use shadow table, ~30 sec

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