Direction Sense

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Direction Sense — Logical Reasoning Questions & Formulas

Logical Reasoning

10 questions

Compass rose with N, NE, E, SE, S, SW, W, NW plus turn rules (facing N a left turn goes to W, a right turn to E; 180 degrees is the opposite; clockwise is right) and shadow rules (sunrise shadow falls west, sunset east, noon shortest).

The One Method: Coordinate / Vector Tracking

Start at $(0,0)$ ; treat N/S as the y-axis and E/W as the x-axis. Add / subtract each leg, then read off the final point. Everything else is a shortcut on top of this.

Coordinate example: 3 km north, then 4 km east, then 3 km south — the north and south legs cancel, leaving 4 km east; when both axes remain, distance equals the square root of x squared plus y squared.

Situation	Rule
All N/S or all E/W	Add / subtract along that one axis
Off both axes	Shortest distance $= \sqrt{x^{2} + y^{2}}$

Angles (clockwise from North): N = 0°, NE = 45°, E = 90°, SE = 135°, S = 180°, SW = 225°, W = 270°, NW = 315°.

Shadows: at sunrise the shadow falls west (facing the sun = facing east); at sunset it falls east; at noon in the tropics it is shortest.

Common Traps

A left / right turn is relative to your current facing, not to North.
"Facing towards" ≠ "walking towards" — don't assume movement happened.
"How far" wants the distance (Pythagoras); "which direction" wants the compass bearing.
Two people → plot both on one grid; comparisons ("who is farther east") read straight off it.

Logical Reasoning

Direction Sense

10 questions

The One Method: Coordinate / Vector Tracking

Start at $(0,0)$ ; treat N/S as the y-axis and E/W as the x-axis. Add / subtract each leg, then read off the final point. Everything else is a shortcut on top of this.

Situation	Rule
All N/S or all E/W	Add / subtract along that one axis
Off both axes	Shortest distance $= \sqrt{x^{2} + y^{2}}$

Angles (clockwise from North): N = 0°, NE = 45°, E = 90°, SE = 135°, S = 180°, SW = 225°, W = 270°, NW = 315°.

Shadows: at sunrise the shadow falls west (facing the sun = facing east); at sunset it falls east; at noon in the tropics it is shortest.

Common Traps

A left / right turn is relative to your current facing, not to North.
"Facing towards" ≠ "walking towards" — don't assume movement happened.
"How far" wants the distance (Pythagoras); "which direction" wants the compass bearing.
Two people → plot both on one grid; comparisons ("who is farther east") read straight off it.