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A person faces South. He turns 90 degrees clockwise, then 180 degrees counter-clockwise, and finally 45 degrees clockwise. Which direction is he facing now?
North-West
South-West
North-East
South-East
North-West
Assign values: Clockwise = positive (+), Counter-clockwise = negative (-). Sum the turns relative to the starting position: South + 90 - 180 + 45 = South - 45 degrees.
Assign values: Clockwise = positive (+), Counter-clockwise = negative (-). Sum the turns relative to the starting position: South + 90 - 180 + 45 = South - 45 degrees.
Initial Position
The person starts facing South (180 degrees on a compass).
Calculate Net Rotation
Total clockwise movement = 90 + 45 = 135 degrees. Total counter-clockwise movement = 180 degrees. Net movement = 135 - 180 = -45 degrees (45 degrees counter-clockwise).
Final Direction Determination
Starting from South, turning 45 degrees counter-clockwise (to the left) points the person towards the South-East quadrant boundary, specifically North-West if viewed from the origin, but let us re-verify: South is 180 deg, -45 deg is 135 deg (South-East). Wait, let's re-calculate: South is 180 deg, +90 = 270 (West), -180 = 90 (East), +45 = 135 (South-East). Let's re-check the compass: South is 180 degrees. 90 deg clockwise = West (270). 180 deg counter-clockwise from West = East (90). 45 deg clockwise from East = South-East (135). Correction: The result is South-East.
A: North-West is the opposite direction of the calculated result. B: South-West is 90 degrees away from the calculated result. C: North-East is 180 degrees away from the calculated result.
D is correct because starting from South (180), turning 90 degrees clockwise leads to West (270), then 180 degrees counter-clockwise leads to East (90), and finally 45 degrees clockwise leads to South-East (135).
When solving direction problems, always use the 360-degree compass method (North=0/360, East=90, South=180, West=270) to avoid confusion between left and right turns.
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