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Jennifer starts from Point D and drives 3 km towards the north. She then takes a left turn and drives 10 km. She then takes another left turn and drives 6 km. She takes one more left turn and drives 5 km. She then takes a right turn and drives 3 km. She takes a final left turn and drives 5 km to reach point E. How far (shortest distance) and towards which direction should she drive in order to reach Point D again? (All turns are 90 degree turns only, unless specified)
6 km North
3 km North
5 km East
5 km North
6 km North
Track net displacement on X (East-West) and Y (North-South) axes independently: Start at (0,0), add movements, and negate the final coordinate to return to origin.
Track net displacement on X (East-West) and Y (North-South) axes independently: Start at (0,0), add movements, and negate the final coordinate to return to origin.
Tracking Cartesian Coordinates
Start at D(0,0). 1: North 3km (0, 3). 2: Left/West 10km (-10, 3). 3: Left/South 6km (-10, -3). 4: Left/East 5km (-5, -3). 5: Right/South 3km (-5, -6). 6: Left/East 5km (0, -6). Point E is at (0, -6).
Calculating Return Distance
Point E is at (0, -6) relative to Point D(0, 0). To reach D(0, 0) from E(0, -6), one must move 6 units in the positive Y direction, which is North.
B: 3 km North is incorrect because the Y-offset is 6 km; C: 5 km East is incorrect as the X-offset is 0; D: 5 km North is incorrect as it fails to cover the full 6 km vertical displacement.
A is correct because the net displacement calculated from point D to point E is 6 km South, meaning she must travel 6 km North to return to point D.
When tracking long paths with multiple turns, always maintain a simple table of North-South and East-West movements to prevent sign errors.
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