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

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

Options:

Correct Answer: 5 km

Solution:

Using the Pythagorean theorem, the shortest distance is 5 km.

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

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

Step 1: Understand that the man walks 3 km north and then 4 km east.
Step 2: Visualize or draw a right triangle where one side is 3 km (north) and the other side is 4 km (east).
Step 3: Identify that the shortest distance back to the starting point is the hypotenuse of this right triangle.
Step 4: Use the Pythagorean theorem, which states that a² + b² = c², where 'a' and 'b' are the two sides and 'c' is the hypotenuse.
Step 5: Calculate: a = 3 km, b = 4 km. So, 3² + 4² = c².
Step 6: Calculate 3² = 9 and 4² = 16. Then add them: 9 + 16 = 25.
Step 7: Find the square root of 25 to get c: √25 = 5 km.
Step 8: Conclude that the shortest distance back to the starting point is 5 km.

Pythagorean Theorem – A mathematical principle used to calculate the length 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 shortest distance between two points in a Cartesian coordinate system.