Mr. Yorly starts from Point A and drives 29 km towards East. He then takes a right turn, drives 16 km, turns right and drives 39 km. He then takes a right turn and drives 9 km. He then takes a right turn, drives 6 km, turns left and drives 3 km. He takes a final right turn, drives 4 km and stops at Point P. How far (shortest distance) and towards which direction should he drive in order to reach Point A again? (All turns are 90 degrees turns only unless specified.)
4 km to the North
Set A at the origin with East as positive x and North as positive y. Track his position after each leg.
Drive 29 km East from A(0, 0) reaches (29, 0), facing East.
Right turn faces South; 16 km leads to (29, \(-16\)).
Right turn faces West; 39 km leads to (\(-10\), \(-16\)).
Right turn faces North; 9 km leads to (\(-10\), \(-7\)).
Right turn faces East; 6 km leads to (\(-4\), \(-7\)).
Left turn faces North; 3 km leads to (\(-4\), \(-4\)).
Final right turn faces East; 4 km leads to P at (0, \(-4\)).
To return to A(0, 0) from P(0, \(-4\)), he must drive 4 km due North.
Hence, the required shortest distance is 4 km to the North.
Similar Questions
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- Read the given paragraph carefully and answer the question.
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Important Questions from Direction and Distance
- Vijendra walks a certain distance, say X metres, from his home towards the west. Then he turns left and walks 23 metres. After that, he turns left and walks 36 metres. Then he turns left again to walk 23 metres. He finally turns left and walks 18 metres to reach his home. Find the value of X.
Gaurav exits from the backdoor of his north-facing house and walks 25 m straight, then he takes a left turn and walks 36 m, then he turns left and walks 47 m. He turns left again and walks 36 m. How far and in which direction is he from his house now?
Reeta is standing facing south-east. First, she turns 135° clockwise. After that, she turns 90 ° anticlockwise. Then she turns 45 ° clockwise, followed by a 135 ° anticlockwise turn. In which direction is she facing now?
Sahasra started running from her house towards the north. After 40 meters she turned left and ran for 75 meters. She then turned right and ran for 30 meters, and again turned right to run 75 meters. In which direction was she running finally?
At the time of sunset, Lopa and Kritika are sitting facing each other. If the shadow of Lopa falls to the right of Kritika, in which direction is Kritika facing?
