If you are at point A and move 3 miles north, then 4 miles west, what is your fi

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Question: If you are at point A and move 3 miles north, then 4 miles west, what is your final position relative to point A?

Options:

Correct Answer: 5 miles northwest

Solution:

Using the Pythagorean theorem, the distance from A is 5 miles northwest.

If you are at point A and move 3 miles north, then 4 miles west, what is your final position relative to point A?

If you are at point A and move 3 miles north, then 4 miles west, what is your final position relative to point A?

Step 1: Start at point A.
Step 2: Move 3 miles north from point A. Now you are at point B.
Step 3: From point B, move 4 miles west. Now you are at point C.
Step 4: To find the distance from point A to point C, use the Pythagorean theorem: a^2 + b^2 = c^2.
Step 5: Here, a is 3 miles (north) and b is 4 miles (west).
Step 6: Calculate: 3^2 + 4^2 = 9 + 16 = 25.
Step 7: Take the square root of 25 to find c: √25 = 5 miles.
Step 8: The direction from point A to point C is northwest.

Pythagorean Theorem – A mathematical principle used to calculate the distance between two points in a right triangle.
Vector Movement – Understanding how to represent movement in terms of direction and distance.
Coordinate Geometry – Using coordinates to determine positions and distances in a two-dimensional space.