Rohit starts at point A and moves 4 km north to reach point B. Then he turns left and moves 3 km west to point C. Next, he turns left again and moves 5 km south to point D. Finally, he turns right and moves 8 km to reach point E.
Sonia wants to travel from point E to point A but cannot cross a mountain directly between these points. She moves 5 km south from E to F, then turns right and moves 6 km to G. From G, she turns left and moves 7 km south to H, then turns right and moves 3 km to I.

What is the shortest distance between point A and point I?

Question

Rohit starts at point A and moves 4 km north to reach point B. Then he turns left and moves 3 km west to point C. Next, he turns left again and moves 5 km south to point D. Finally, he turns right and moves 8 km to reach point E.
Sonia wants to travel from point E to point A but cannot cross a mountain directly between these points. She moves 5 km south from E to F, then turns right and moves 6 km to G. From G, she turns left and moves 7 km south to H, then turns right and moves 3 km to I.

What is the shortest distance between point A and point I?

Accepted Answer

**Solution:**

1. First, determine the coordinates of points relative to A, assuming A at origin (0,0).

- Rohit's path:
  - From A (0,0) move 4 km north to B (0,4)
  - Turn left (west), move 3 km to C (-3,4)
  - Turn left (south), move 5 km to D (-3,-1)
  - Turn right (west), move 8 km to E (-11,-1)

2. Sonia's path from E (-11,-1):
  - Moves 5 km south to F (-11,-6)
  - Turns right (west to north? Since facing south, right turn is west to north? Actually, facing south, right turn is west to west? Let's clarify directions carefully.)

Let's clarify Sonia's directions:
  - From E, she moves 5 km south to F (-11,-6)
  - From F, she turns right. Since she was moving south, turning right means west to west? Actually, if facing south, right turn is west.
  - Moves 6 km west to G (-17,-6)
  - From G, turns left (facing west, left turn is south)
  - Moves 7 km south to H (-17,-13)
  - From H, turns right (facing south, right turn is west)
  - Moves 3 km west to I (-20,-13)

3. Point A is at (0,0), point I is at (-20,-13).

4. Calculate the shortest distance between A and I using distance formula:

$$
	ext{Distance} = \sqrt{(-20 - 0)^2 + (-13 - 0)^2} = \sqrt{400 + 169} = \sqrt{569}
$$

**Answer:** $\sqrt{569} 	ext{ km}$

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