If you are at point A and move 3 units east and 4 units north, what is your new

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Question: If you are at point A and move 3 units east and 4 units north, what is your new position relative to point A?

Options:

Correct Answer: 5 units northeast

Solution:

Using the Pythagorean theorem, the distance is 5 units northeast.

If you are at point A and move 3 units east and 4 units north, what is your new position relative to point A?

If you are at point A and move 3 units east and 4 units north, what is your new position relative to point A?

Step 1: Start at point A, which we can call the origin (0, 0).
Step 2: Move 3 units east. This means you go from (0, 0) to (3, 0).
Step 3: Now, from (3, 0), move 4 units north. This means you go from (3, 0) to (3, 4).
Step 4: Your new position is (3, 4) relative to point A.
Step 5: To find the distance from point A to your new position, use the Pythagorean theorem: distance = sqrt((3^2) + (4^2)).
Step 6: Calculate 3^2 = 9 and 4^2 = 16, then add them: 9 + 16 = 25.
Step 7: Take the square root of 25, which is 5. So, the distance is 5 units.
Step 8: The direction from point A to your new position is northeast.

Coordinate Geometry – Understanding movement in a 2D plane using directional vectors.
Pythagorean Theorem – Calculating the distance between two points using the formula a² + b² = c².