Simar starts from Point A and drives 10 km towards south. He then takes a right turn, drives 7 km, turns right and drives 12 km. He then takes a right turn and drives 9 km. He takes a final right turn, drives 2 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.)
2 km to the west
3 km to the west
2 km to the east
3 km to the east
The correct option is 2 km to the west.
Let us trace Simar's path step-by-step from the starting point A, using a standard two-dimensional coordinate system where the starting point A is at the origin (0, 0). Let the positive y-axis represent North, negative y-axis represent South, positive x-axis represent East, and negative x-axis represent West.
All turns are 90-degree turns.
Step 1: Drives 10 km towards south from Point A.
Starting at A(0, 0) and moving south (negative y-direction) by 10 km, Simar reaches coordinate:
(0, -10)
Step 2: Takes a right turn and drives 7 km.
Facing south, a right turn points towards the West (negative x-direction). Moving 7 km in this direction, Simar reaches:
(0 - 7, -10) = (-7, -10)
Step 3: Turns right and drives 12 km.
Facing west, a right turn points towards the North (positive y-direction). Moving 12 km in this direction, Simar reaches:
(-7, -10 + 12) = (-7, 2)
Step 4: Takes a right turn and drives 9 km.
Facing north, a right turn points towards the East (positive x-direction). Moving 9 km in this direction, Simar reaches:
(-7 + 9, 2) = (2, 2)
Step 5: Takes a final right turn, drives 2 km and stops at Point P.
Facing east, a right turn points towards the South (negative y-direction). Moving 2 km in this direction, Simar reaches Point P at:
(2, 2 - 2) = (2, 0)
Determining the shortest distance and direction from Point P to Point A:
Point A is located at (0, 0) and Point P is located at (2, 0).
Since both points lie on the x-axis (y = 0), the shortest path is a straight horizontal line.
The distance between P(2, 0) and A(0, 0) is:
To go from P(2, 0) to A(0, 0), Simar must travel in the negative x-direction, which represents West.
Therefore, he should drive 2 km to the west to reach Point A again.
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