If a person walks 5 km north and then 5 km east, how far is he from the starting

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Question: If a person walks 5 km north and then 5 km east, how far is he from the starting point?

Options:

Correct Answer: 7.5 km

Solution:

Using the Pythagorean theorem, the distance is √(5^2 + 5^2) = √50 = 7.5 km.

If a person walks 5 km north and then 5 km east, how far is he from the starting point?

If a person walks 5 km north and then 5 km east, how far is he from the starting point?

Step 1: Understand that the person walks 5 km north and then 5 km east.
Step 2: Visualize the path as a right triangle where one leg is 5 km (north) and the other leg is 5 km (east).
Step 3: Use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the distance from the starting point) is equal to the sum of the squares of the other two sides.
Step 4: Calculate the squares of the two legs: 5^2 = 25 and 5^2 = 25.
Step 5: Add the squares together: 25 + 25 = 50.
Step 6: Take the square root of 50 to find the distance: √50.
Step 7: Simplify √50 to get approximately 7.07 km (or 7.5 km when rounded).

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 using coordinates.