Shivani drives 17 km to the North, then drives 9 km East, and then drives 17 km South.
How far is Shivani from the starting point when considered in a straight line?
Correct Answer :
9 km
Solution :
The correct answer is 9 km.
Let us trace Shivani's path step-by-step to determine her final position relative to the starting point:
1. First leg of the journey: Shivani starts at a point, let's call it . She drives 17 km to the North, arriving at point . The distance in the North direction.
2. Second leg of the journey: From point , she turns and drives 9 km to the East, arriving at point . The distance in the East direction.
3. Third leg of the journey: From point , she turns and drives 17 km to the South, arriving at her final destination, point . The distance in the South direction.
Since North and South are opposite directions, the 17 km drive South directly cancels out the 17 km drive North in terms of vertical displacement.
This forms a rectangle , where:
- The North-South sides are equal: .
- The East-West sides must also be equal: .
Therefore, the straight-line distance from the starting point to the final point is equal to , which is 9 km.
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