A person walks 5 km north, then 5 km west. What is the shortest distance back to

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Question: A person walks 5 km north, then 5 km west. What is the shortest distance back to the starting point?

Options:

Correct Answer: 7.07 km

Solution:

The shortest distance back is the hypotenuse of a right triangle, which is 7.07 km.

A person walks 5 km north, then 5 km west. What is the shortest distance back to the starting point?

A person walks 5 km north, then 5 km west. What is the shortest distance back to the starting point?

Step 1: Understand that the person walks 5 km north and then 5 km west.
Step 2: Visualize the path as two sides of a right triangle, where one side is 5 km (north) and the other side is 5 km (west).
Step 3: Use the Pythagorean theorem to find the hypotenuse (the shortest distance back). The formula is a^2 + b^2 = c^2, where a and b are the two sides.
Step 4: Calculate 5^2 + 5^2 = 25 + 25 = 50.
Step 5: Find the square root of 50 to get the length of the hypotenuse: √50 = 7.07 km.
Step 6: Conclude that the shortest distance back to the starting point is 7.07 km.

Pythagorean Theorem – The relationship between the lengths of the sides of a right triangle, where 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 or geometric principles.