This problem involves tracking the movement of a person named Amit based on directional instructions and calculating the final displacement from his starting point.

Mapping Amit's Path

Let's trace Amit's journey step-by-step, assuming his starting point A is at the origin (0, 0) on a 2D plane. East corresponds to the positive x-axis, West to the negative x-axis, North to the positive y-axis, and South to the negative y-axis.

• Point A (Start): Amit starts at point A. We can represent this as coordinate (0, 0).
• A to B: Amit walks 10 m towards East.
  • New position: (0 + 10, 0) = (10, 0). This is point B.
• B to C: From point B, Amit takes a right turn. Since he was facing East, a right turn means he now faces South. He walks 10 m South.
  • New position: (10, 0 - 10) = (10, -10). This is point C.
• C to D: From point C, he takes another right turn. Facing South, a right turn means he now faces West. He walks 5 m West.
  • New position: (10 - 5, -10) = (5, -10). This is point D.
• D to E: From point D, he again takes a right turn. Facing West, a right turn means he now faces North. He walks 5 m North.
  • New position: (5, -10 + 5) = (5, -5). This is point E.
• E to F: From point E, he takes a left turn. Facing North, a left turn means he now faces West. He walks 5 m West.
  • New position: (5 - 5, -5) = (0, -5). This is the end point F.

Calculating the Distance

We need to find the distance between the starting point A (0, 0) and the end point F (0, -5). We can use the distance formula, which is derived from the Pythagorean theorem.

The distance formula between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Here, $(x_1, y_1) = (0, 0)$ (Point A) and $(x_2, y_2) = (0, -5)$ (Point F).

Plugging these values into the formula:

$$ d = \sqrt{(0 - 0)^2 + (-5 - 0)^2} $$

$$ d = \sqrt{(0)^2 + (-5)^2} $$

$$ d = \sqrt{0 + 25} $$

$$ d = \sqrt{25} $$

$$ d = 5 \text{ m} $$

The distance between the starting point A and the end point F is 5 meters.