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If a person walks 12 meters towards the South and then 5 meters towards the East

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Question: If a person walks 12 meters towards the South and then 5 meters towards the East, what is the shortest distance back to the starting point? (2023)

Options:

  1. 13 meters
  2. 17 meters
  3. 12 meters
  4. 5 meters

Correct Answer: 13 meters

Exam Year: 2023

Solution: 

Using the Pythagorean theorem, the distance back is √(12^2 + 5^2) = √(144 + 25) = √169 = 13 meters.

If a person walks 12 meters towards the South and then 5 meters towards the East

Practice Questions

Q1
If a person walks 12 meters towards the South and then 5 meters towards the East, what is the shortest distance back to the starting point? (2023)
  1. 13 meters
  2. 17 meters
  3. 12 meters
  4. 5 meters

Questions & Step-by-Step Solutions

If a person walks 12 meters towards the South and then 5 meters towards the East, what is the shortest distance back to the starting point? (2023)
  • Step 1: Understand the problem. A person walks 12 meters South and then 5 meters East.
  • Step 2: Visualize the path. The person creates a right triangle where one side is 12 meters (South) and the other side is 5 meters (East).
  • Step 3: Identify the sides of the triangle. The vertical side (South) is 12 meters, and the horizontal side (East) is 5 meters.
  • Step 4: Use the Pythagorean theorem to find the shortest distance back to the starting point. The theorem states that the square of the hypotenuse (the distance back) is equal to the sum of the squares of the other two sides.
  • Step 5: Calculate the squares of the sides: 12^2 = 144 and 5^2 = 25.
  • Step 6: Add the squares together: 144 + 25 = 169.
  • Step 7: Take the square root of the sum to find the hypotenuse: √169 = 13.
  • Step 8: Conclude that the shortest distance back to the starting point is 13 meters.
  • Pythagorean Theorem – A mathematical principle used to calculate the length of the sides of a right triangle, specifically relating the lengths of the legs to the hypotenuse.
  • Distance Calculation – Understanding how to calculate the shortest distance between two points in a coordinate system.
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