If you are at point A and move 3 km south, then 4 km west, where are you relativ

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

Options:

Correct Answer: 5 km South-West

Solution:

You are 5 km away in the south-west direction from point A.

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

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

Step 1: Start at point A.
Step 2: Move 3 km directly south from point A. You are now at point B.
Step 3: From point B, move 4 km directly west. You are now at point C.
Step 4: To find out where point C is relative to point A, visualize or draw a right triangle.
Step 5: The south movement (3 km) is one side of the triangle, and the west movement (4 km) is the other side.
Step 6: Use the Pythagorean theorem to find the distance from point A to point C: distance = sqrt(3^2 + 4^2).
Step 7: Calculate: 3^2 = 9, 4^2 = 16, so 9 + 16 = 25. The square root of 25 is 5.
Step 8: The distance from point A to point C is 5 km.
Step 9: Determine the direction: you moved south and west, which means you are in the south-west direction from point A.

Coordinate Geometry – Understanding movement in a Cartesian plane and calculating distances using the Pythagorean theorem.
Vector Addition – Combining movements in different directions to determine the final position relative to the starting point.