A person walks 10 m North, then turns left and walks 10 m, then turns left and walks 5 m, then turns left and walks 15 m. How far is he from the starting point?
- 5 m
- 7.07 m
- 10 m
- 15 m
Explanation
Step 1: Define Movements on a Coordinate System
- Let the starting point be at the origin (0,0) We can track the person's position by adding the vectors of each movement:
- 10 m North: The position becomes (0.10)
- Turn left (West) and walk 10 m: The position becomes (10.10)
- Turn left (South) and walk 5 m: The position becomes (-10, 5)
- Turn left (East) and walk 15 m: The position becomes (10, 15, 5) = (5, 5)
Step 2: Calculate the Straight-Line Distance
To find the distance from the starting point (0,0) to the final point (5, 5), we use the distance formula:
d = √(x2 - x1 )^2 + ( y2 - y 1) ^2
d = √(5-0)^2 ( 5-0) ^2
d= √(5^2 + 5^2)
d= √(25 + 25)
d= √(50)
Simplifying the radical gives:
d = 5 √2
The person is 5 √2 (which is approximately 7.07 m) away from the starting point.
Last updated 05-03-2026
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