A person walks 6 km south, then 8 km west. How far is he from the starting point

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Question: A person walks 6 km south, then 8 km west. How far is he from the starting point?

Options:

Correct Answer: 10 km

Solution:

Using the Pythagorean theorem, the distance is √(6^2 + 8^2) = 10 km.

A person walks 6 km south, then 8 km west. How far is he from the starting point?

A person walks 6 km south, then 8 km west. How far is he from the starting point?

Step 1: Understand the problem. The person walks 6 km south and then 8 km west.
Step 2: Visualize the path. Imagine a right triangle where one side is 6 km (south) and the other side is 8 km (west).
Step 3: Identify the sides of the triangle. The south distance (6 km) is one side, and the west distance (8 km) is the other side.
Step 4: Use the Pythagorean theorem. This theorem 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 5: Write the equation. The equation is: distance^2 = (6 km)^2 + (8 km)^2.
Step 6: Calculate the squares. (6 km)^2 = 36 and (8 km)^2 = 64.
Step 7: Add the squares together. 36 + 64 = 100.
Step 8: Find the square root. The square root of 100 is 10.
Step 9: Conclusion. The distance from the starting point is 10 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 or geometric principles.