If you are at point A and move 3 km east, then 4 km north, where are you relativ

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Question: If you are at point A and move 3 km east, then 4 km north, where are you relative to point A?

Options:

Correct Answer: 5 km North-East

Solution:

The distance from point A is 5 km in the north-east direction, calculated using the Pythagorean theorem.

If you are at point A and move 3 km east, then 4 km north, where are you relative to point A?

If you are at point A and move 3 km east, then 4 km north, where are you relative to point A?

Step 1: Start at point A.
Step 2: Move 3 km to the east. Now you are at point B, which is 3 km east of point A.
Step 3: From point B, move 4 km to the north. Now you are at point C, which is 4 km north of point B.
Step 4: To find out how far you are from point A, imagine a right triangle where one side is 3 km (east) and the other side is 4 km (north).
Step 5: Use the Pythagorean theorem: a² + b² = c², where a = 3 km, b = 4 km.
Step 6: Calculate: 3² + 4² = 9 + 16 = 25.
Step 7: Find c by taking the square root of 25: √25 = 5 km.
Step 8: You are 5 km away from point A in the north-east direction.

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.
Vector Addition – Understanding how to combine movements in different directions to find a resultant position.
Coordinate Geometry – Using a coordinate system to determine positions and distances based on directional movement.