The front door of Mr. X's house faces East. Mr. X leaves the house, walking 50m straight from the back door that is situated directly opposite to the front door. He then turns to his right, walks for another 50m and stops. The direction of the point Mr. X is now located at with respect to the starting point is _______.
A. South-East B. North-East C. West D. North-West
GATE 2021 · General Aptitude · Direction Sense · medium
Answer: The final position is North-West of the starting point. Answer: D. North-West.
Identify initial walking direction from back door: Front door faces East => back door faces West. Mr. X exits back door and walks 50m heading West. Let start = (0, 0). After first leg: position = (-50, 0).
Apply right turn from westward heading: Mr. X was facing West. Turning right rotates 90 degrees clockwise: West -> North. He then walks 50m North. New position = (-50, 0) + (0, 50) = (-50, 50).
Determine final direction from starting point: Final position relative to start = (-50, 50). x is negative (West), y is positive (North). This places the point in the North-West quadrant. The angle is exactly 135 degrees from East, or 45 degrees West of North = North-West.