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

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Question: A person travels 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 √(3² + 4²) = 5 km.

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

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

Step 1: Understand that the person travels 3 km north and then 4 km east.
Step 2: Visualize the path as a right triangle, where one side is 3 km (north) and the other side is 4 km (east).
Step 3: Use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the shortest distance back) is equal to the sum of the squares of the other two sides.
Step 4: Calculate the squares of the two sides: 3² = 9 and 4² = 16.
Step 5: Add the squares together: 9 + 16 = 25.
Step 6: Take the square root of the sum to find the hypotenuse: √25 = 5 km.
Step 7: Conclude that the shortest distance back to the starting point is 5 km.

Pythagorean Theorem – The theorem relates the lengths of the sides of a right triangle, stating that the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Distance Calculation – Understanding how to calculate the straight-line distance between two points in a coordinate system.