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The image you uploaded contains several transformation problems involving coordinates and graphs. Let's go through each problem step by step:

### Problem 6 (Transformation: Reflection over x-axis)
- Original coordinates of points A, B, C, D for quadrilateral ABCD are:
  - A (1, 4)
  - B (4, 4)
  - C (4, 2)
  - D (1, 2)
  
After reflecting over the x-axis, we change the y-coordinates' sign while keeping the x-coordinates the same. The new coordinates of A'B'C'D' are:
  - A' (1, -4)
  - B' (4, -4)
  - C' (4, -2)
  - D' (1, -2)

### Problem 7 (Transformation: Reflection over y-axis)
- Original coordinates of points A, B, C, D are:
  - A (2, 1)
  - B (5, 1)
  - C (5, 6)
  - D (2, 6)

After reflecting over the y-axis, we change the x-coordinates' sign while keeping the y-coordinates the same. The new coordinates of A'B'C'D' are:
  - A' (-2, 1)
  - B' (-5, 1)
  - C' (-5, 6)
  - D' (-2, 6)

### Problem 8 (Transformation: Translation by the rule (x, y) → (x + 7, y + 6))
- Original coordinates of points A, B, C, D are:
  - A (-8, 5)
  - B (-4, 2)
  - C (2, -1)
  - D (1, -4)

After translating the shape according to the rule, add 7 to the x-coordinate and 6 to the y-coordinate:
  - A' (-8 + 7, 5 + 6) = (-1, 11)
  - B' (-4 + 7, 2 + 6) = (3, 8)
  - C' (2 + 7, -1 + 6) = (9, 5)
  - D' (1 + 7, -4 + 6) = (8, 2)

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Would you like to go over the details of the transformations or have any specific questions about the graphing?

### Additional Questions:
1. How does reflection across the x-axis change coordinates?
2. How can you verify your translation results on the graph?
3. What are other types of transformations besides reflection and translation?
4. How do the rules of translation affect the orientation of the shape?
5. What happens if you reflect over both axes (x and y) sequentially?

**Tip**: For reflections, always remember that x-axis affects y-coordinates, and y-axis affects x-coordinates when flipping across these lines!

Solve transformation problems involving reflection over the x-axis, reflection over the y-axis, and translation on a coordinate plane.

This guide helps you solve transformation problems including reflection over the x-axis, reflection over the y-axis, and translation of shapes on a coordinate plane. Explore the mathematical rules behind transformations, reflections, and translations, with step-by-step solutions. Ideal for students in Grades 8-10.

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