If a person walks 10 km north, then 10 km east, how far is he from the starting

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Question: If a person walks 10 km north, then 10 km east, how far is he from the starting point?

Options:

Correct Answer: 14.14 km

Solution:

Using Pythagorean theorem: distance = √(10^2 + 10^2) = √200 = 14.14 km.

If a person walks 10 km north, then 10 km east, how far is he from the starting point?

If a person walks 10 km north, then 10 km east, how far is he from the starting point?

Step 1: Understand that the person walks 10 km north and then 10 km east.
Step 2: Visualize the path as a right triangle where one leg is 10 km (north) and the other leg is 10 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: 10^2 = 100 and 10^2 = 100.
Step 5: Add the two squares together: 100 + 100 = 200.
Step 6: Take the square root of 200 to find the distance: √200 = 14.14 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 Cartesian coordinate system.