Anil starts from point A and drives 8 km towards North. He then takes a right turn, drives 2 km, turns right and drives 11 km. He then takes a right turn and drives 5 km. He takes a final right turn, drives 3 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.)
Correct Answer :
3 km towards East
Solution :
The correct option is 3 km towards East.
To find the shortest distance and direction from the final position P to the starting point A, we can map the entire journey on a two-dimensional coordinate system. Let us set the starting point A at the origin where:
- North corresponds to the positive y-axis.
- South corresponds to the negative y-axis.
- East corresponds to the positive x-axis.
- West corresponds to the negative x-axis.
Let's trace Anil's path step-by-step:
1. Start at Point A: .
2. Drive 8 km North: Moving along the positive y-axis brings Anil to:
.
3. Turn right and drive 2 km: A right turn from North is East (positive x-direction). Moving 2 km East brings him to:
.
4. Turn right and drive 11 km: A right turn from East is South (negative y-direction). Moving 11 km South brings him to:
.
5. Turn right and drive 5 km: A right turn from South is West (negative x-direction). Moving 5 km West brings him to:
.
6. Turn right and drive 3 km to stop at P: A right turn from West is North (positive y-direction). Moving 3 km North brings him to his final point P:
.
Now, we find the relative position of the starting point A from point P :
- The difference in x-coordinates is km (towards the positive x-direction, which is East).
- The difference in y-coordinates is km.
Thus, point P is located 3 km West of point A. In order to return to point A from point P, Anil must travel a shortest distance of 3 km towards East.
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