https://file.aiquickdraw.com/mathbot/file/173022790600708ka7szk.jpg

The question asks about the distance from the boy's original position after he walked in two perpendicular directions. Let’s analyze this step-by-step.

1. **Setup**:
   - The boy turns 90 degrees, forming a right angle in his path.
   - He walks 12 km in one direction and, after turning, continues another 12 km in the perpendicular direction.

2. **Calculation**:
   Since the two legs of his journey form a right triangle, with each leg being 12 km, we can use the Pythagorean theorem to find the hypotenuse \(c\), which represents the straight-line distance from his starting point:
   \[
   c = \sqrt{12^2 + 12^2} = \sqrt{144 + 144} = \sqrt{288} \approx 16.97 \text{ km}
   \]

3. **Answer**:
   Rounding to the nearest kilometer, the answer is approximately **17 km**. However, based on the choices given in the image, the closest answer provided is **16 km**.

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Here are some follow-up questions to expand on this problem:

1. How would the answer change if the boy walked different distances in each direction?
2. What if the boy turned by 45 degrees instead of 90 degrees after the first segment of his walk?
3. Can you use trigonometric functions to verify the distance calculated here?
4. How is the Pythagorean theorem applied when finding distances on a coordinate plane?
5. What if there were three turns, each with a different distance? How would you calculate the final position?

**Tip**: When dealing with paths forming right angles, always think about the Pythagorean theorem if you're asked for a straight-line distance.

He turned to face his original position, then turned 90 degrees clockwise and walked for 12 km. To the nearest kilometre, how far is the boy from his original position?

Learn how to calculate the distance from the original position using the Pythagorean theorem when moving at a 90-degree angle. The boy walks two 12 km segments, forming a right triangle. This problem is suitable for Grade 10 students and covers essential geometry concepts.

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