**Amit started walking towards West direction from point A. After**

**walking 17 m he reached point B, from there he takes a right**

**turn and walk 11 m to reach point C. From C, he turns left and**

**walk 9 m and reaches point D. Then, he turns left and walks 25**

**m to reach point E. From point E he turns left and walks 32 m.**

**Now he reached point F and from there he turns left and walks**

**30 m to reach point G. From point G he turns left and walks 2 m**

**to reach point H.**

**8. What is the direction of G with respect to A?**

**(a) Northeast (b) East (c) Northwest (d) West (e) Southwest**

**9. What is the distance between A and H and A is in which**

**direction with respect to H?**

**(a) √273m southeast (b) √270m southeast (c) √269m southwest**

**(d) √172m southeast (e) √272m southwest**

Let's break down the problem step by step to determine the direction of point G with respect to point A and the distance between points A and H.

### Step 1: Understanding the Directions
1. **Amit starts at point A** and walks **17 meters West** to reach point B.
2. From B, he takes a **right turn (North)** and walks **11 meters** to reach point C.
3. From C, he turns **left (West)** and walks **9 meters** to reach point D.
4. From D, he turns **left (South)** and walks **25 meters** to reach point E.
5. From E, he turns **left (East)** and walks **32 meters** to reach point F.
6. From F, he turns **left (North)** and walks **30 meters** to reach point G.
7. Finally, from G, he turns **left (West)** and walks **2 meters** to reach point H.

### Step 2: Position Analysis

- **Point A:** Starting position.
- **Point B:** \(17 \, \text{m} \) west of A.
- **Point C:** \(17 \, \text{m} \) west and \(11 \, \text{m} \) north of A.
- **Point D:** \(26 \, \text{m} \) west and \(11 \, \text{m} \) north of A.
- **Point E:** \(26 \, \text{m} \) west and \(14 \, \text{m} \) south of A.
- **Point F:** \(6 \, \text{m} \) east and \(14 \, \text{m} \) south of A.
- **Point G:** \(6 \, \text{m} \) east and \(16 \, \text{m} \) north of A.
- **Point H:** \(4 \, \text{m} \) west and \(16 \, \text{m} \) north of A.

### Step 3: Calculating the Answers

1. **Direction of G with respect to A:**
   - G is located to the **East (6 meters)** and **North (16 meters)** of A.
   - This direction corresponds to **Northeast**.
   - **Answer:** (a) Northeast.

2. **Distance between A and H:**
   - H is located \(4 \, \text{m} \) west and \(16 \, \text{m} \) north of A.
   - The distance between A and H can be calculated using the Pythagorean theorem:

   \[
   \text{Distance} = \sqrt{(16^2 + 4^2)} = \sqrt{256 + 16} = \sqrt{272 \, \text{m}}
   \]

   - **Direction of A with respect to H:** Since H is to the north and west of A, A is to the **Southeast** of H.
   - **Answer:** (e) \(\sqrt{272} \, \text{m} \) southeast.

### Final Answers:
1. **Direction of G with respect to A:** (a) Northeast.
2. **Distance between A and H and direction of A with respect to H:** (e) \(\sqrt{272} \, \text{m} \) southeast.

Would you like any more details or have further questions? 

Here are 8 questions related to the above:

1. How is the Pythagorean theorem used to calculate distances?
2. What are the cardinal directions and how are they used in navigation?
3. How can a sequence of movements be represented on a coordinate plane?
4. How do you calculate the total distance traveled in a problem like this?
5. What are the steps to determine direction between two points?
6. How can this problem be solved using vector addition?
7. What is the significance of right and left turns in navigation problems?
8. How does understanding geometry help in solving such problems?

**Tip:** Drawing a diagram or map can help visualize complex movement problems and make it easier to calculate directions and distances.

Learn how to solve a problem involving directions and distances based on Amit's movements from point A to H. This problem utilizes concepts from coordinate geometry, including the distance formula and the Pythagorean theorem. Suitable for students in Grades 7-9.

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