If you move 3 miles east and then 4 miles north, how far are you from your start

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Question: If you move 3 miles east and then 4 miles north, how far are you from your starting point?

Options:

Correct Answer: 5 miles

Solution:

Using the Pythagorean theorem, the distance is √(3^2 + 4^2) = 5 miles.

If you move 3 miles east and then 4 miles north, how far are you from your starting point?

If you move 3 miles east and then 4 miles north, how far are you from your starting point?

Step 1: Start at your starting point. Imagine this point as (0, 0) on a graph.
Step 2: Move 3 miles east. This means you go to the point (3, 0).
Step 3: From (3, 0), move 4 miles north. Now you are at the point (3, 4).
Step 4: To find out how far you are from the starting point (0, 0) to (3, 4), use the Pythagorean theorem.
Step 5: The formula is distance = √(x^2 + y^2), where x is the east movement and y is the north movement.
Step 6: Plug in the values: distance = √(3^2 + 4^2).
Step 7: Calculate 3^2 = 9 and 4^2 = 16.
Step 8: Add these two results: 9 + 16 = 25.
Step 9: Take the square root of 25, which is 5.
Step 10: Therefore, you are 5 miles away from your starting point.

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.