A person walks 3 km north, then 4 km east. What is the shortest distance back to

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Question: A person walks 3 km north, then 4 km east. What is the shortest distance back to the starting point?

Options:

Correct Answer: 5 km

Solution:

Using the Pythagorean theorem, the distance is 5 km.

A person walks 3 km north, then 4 km east. What is the shortest distance back to the starting point?

A person walks 3 km north, then 4 km east. What is the shortest distance back to the starting point?

Step 1: Understand the person's movement. They walk 3 km north and then 4 km east.
Step 2: Visualize the path. The person creates a right triangle where one side is 3 km (north) and the other side is 4 km (east).
Step 3: Identify the right triangle. The distance back to the starting point is the hypotenuse of this triangle.
Step 4: Use the Pythagorean theorem, which states that a² + b² = c², where 'c' is the hypotenuse.
Step 5: Calculate a² + b². Here, a = 3 km and b = 4 km. So, 3² + 4² = 9 + 16 = 25.
Step 6: Find the hypotenuse 'c' by taking the square root of 25. So, c = √25 = 5 km.
Step 7: Conclude that the shortest distance back to the starting point is 5 km.

Pythagorean Theorem – The theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
Distance Calculation – Understanding how to calculate the shortest distance between two points using geometric principles.