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

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

Options:

Correct Answer: 14.14 km

Solution:

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

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

If a person walks 10 km north and 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: Write the equation: Distance^2 = (10 km)^2 + (10 km)^2.
Step 5: Calculate (10 km)^2, which is 100 km^2. So, you have: Distance^2 = 100 + 100.
Step 6: Add the two values: Distance^2 = 200 km^2.
Step 7: To find the distance, take the square root of 200 km^2: Distance = √200.
Step 8: Calculate √200, which is approximately 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 using coordinates.