Question Details

Ajay starts from Point A and drives 6 km towards north. He then takes a left turn, drives 5 km, turns left and drives 15 km. He then takes a left turn and drives 12 km. He takes a final left turn, drives 9 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° turns only unless specified.)

Options

A

6 km to the east

B

6 km to the west

C

7 km to the east

D

7 km to the west

Show Answer

Correct Answer :

Option D

7 km to the west

7 km to the west

Solution :

To find the shortest distance and direction Ajay needs to drive to return to Point A from Point P, we can track his path step-by-step on a standard two-dimensional coordinate system. Let Point A be the origin (0,0).

Let's define the directions as follows:
- North corresponds to the positive y-axis direction.
- South corresponds to the negative y-axis direction.
- East corresponds to the positive x-axis direction.
- West corresponds to the negative x-axis direction.

Now, let's trace Ajay's movements sequentially:

1. Start at Point A:
Position is (0,0).

2. Drive 6 km towards North:
He moves 6 units up along the y-axis.
New position: (0,6).

3. Turn left and drive 5 km:
Facing North, a left turn points West (negative x-axis). He moves 5 units to the left.
New position: (0-5,6)=(-5,6).

4. Turn left and drive 15 km:
Facing West, a left turn points South (negative y-axis). He moves 15 units down.
New position: (-5,6-15)=(-5,-9).

5. Turn left and drive 12 km:
Facing South, a left turn points East (positive x-axis). He moves 12 units to the right.
New position: (-5+12,-9)=(7,-9).

6. Take a final left turn and drive 9 km to Point P:
Facing East, a left turn points North (positive y-axis). He moves 9 units up.
Position of Point P: (7,-9+9)=(7,0).

Now, we compare the final coordinates of Point P and the starting Point A:
- Point P is at (7,0).
- Point A is at (0,0).

To go from Point P (7,0) back to Point A (0,0), Ajay must travel along the x-axis from x=7 to x=0.
Distance = 7-0=7 km.
Since he is moving in the negative x-direction (from 7 to 0), the direction is West.

Therefore, Ajay should drive 7 km to the west to reach Point A again.

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