A person walks 12 km east and then 5 km south. What is the shortest distance bac

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Question: A person walks 12 km east and then 5 km south. What is the shortest distance back to the starting point?

Options:

Correct Answer: 13 km

Solution:

Using the Pythagorean theorem, the distance is √(12² + 5²) = 13 km.

A person walks 12 km east and then 5 km south. What is the shortest distance back to the starting point?

A person walks 12 km east and then 5 km south. What is the shortest distance back to the starting point?

Step 1: Understand that the person walks 12 km east and then 5 km south, creating a right triangle.
Step 2: Identify the two sides of the triangle: one side is 12 km (east) and the other side is 5 km (south).
Step 3: Use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
Step 4: Write the formula: Distance = √(12² + 5²).
Step 5: Calculate 12², which is 144.
Step 6: Calculate 5², which is 25.
Step 7: Add the two results: 144 + 25 = 169.
Step 8: Take the square root of 169, which is 13.
Step 9: Conclude that the shortest distance back to the starting point is 13 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 straight-line distance between two points using coordinates.