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Examoogle • User • info@examoogle.com • EE-2024-8821
Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked
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Ashutosh starts from Point A and drives 19 km towards West. He then takes a left turn, drives 9 km, turns left and drives 26 km. He then takes a left turn and drives 19 km. He takes a final left turn, drives 7 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-degree turns only, unless specified.)
11 km to the South
11 km to the North
10 km to the North
10 km to the South
10 km to the South
Track the net displacement using coordinates: set start point A at (0,0). Sum movements: West is -X, East is +X, North is +Y, South is -Y.
Track the net displacement using coordinates: set start point A at (0,0). Sum movements: West is -X, East is +X, North is +Y, South is -Y.
Coordinate Mapping
Start A at (0,0). Moves: 1. 19 km West (-19, 0). 2. Left (South)₉ km (-19, -9). 3. Left (East)₂₆ km (-19+26 = 7, -9). 4. Left (North)₁₉ km (7, -9+19 = 10). 5. Left (West)₇ km (7-7 = 0, 10). Wait, re-reading: Ashutosh is at (0, 10). Distance is 10 km South.
Net Result Calculation
Ashutosh's final position P relative to A(0,0) is (0, 10). Since the X-coordinate is 0 and Y-coordinate is +10 (North), he must move 10 km South to reach (0,0).
A: 11 km South is incorrect; the Y-displacement is exactly 10 km. B: 11 km North increases the gap to 21 km. C: 10 km North would move him to 20 km North of A.
D is correct because his final position is 10 km exactly North of Point A, requiring a 10 km movement to the South to return to the start.
Always assign coordinates (0,0) to the starting point to handle multiple turns without losing track of relative distance.