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The exercise you’ve shared asks about transformations between pairs of shapes. The transformations could involve translations (slides), rotations, reflections (flips), or dilations (rescaling). Let's address each problem one by one:

### Problem 1:
- **Are the red and purple triangles related by a transformation?**
  - Yes, these triangles are related by a **rotation**. The red triangle can be rotated 90 degrees counterclockwise around point \( G \), and it will match the purple triangle exactly.

### Problem 2:
- **Are the red and purple "L" shapes related by a transformation?**
  - Yes, the red "L" shape can be transformed into the purple "L" shape through a **translation** (shift). If you move the red shape down and to the right, it will coincide with the purple shape. No rotation, reflection, or dilation is necessary.

### Problem 3:
- **Are the red and purple triangles related by a transformation?**
  - No, the red and purple triangles cannot be mapped onto each other by any combination of translation, rotation, reflection, or dilation. Their orientations and sizes differ significantly.

### Problem 4:
- **Are the red and purple rectangles related by a transformation?**
  - No, these rectangles cannot be related by a simple transformation. The red rectangle is significantly larger than the purple one, and no combination of transformations like translation or reflection can match their sizes without a dilation. However, even with dilation, their aspect ratios (length-to-width ratio) differ, making it impossible.

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Would you like more details on any of these transformations?

### 5 Related Questions:
1. What are the steps involved in identifying a rotation between two shapes?
2. Can shapes be mapped onto each other using multiple transformations at once?
3. How do you recognize when a dilation is necessary?
4. What is the difference between reflection and rotation in transformations?
5. Can transformations be combined in a sequence, and how is this done?

### Tip:
Always check both the orientation and size of shapes before deciding on the transformation type. This helps in determining whether a rotation, translation, or dilation is needed.

Is there a transformation or sequence of translations, rotations, reflections, or dilations that moves one figure onto the other?

This exercise explores geometric transformations between pairs of shapes on a coordinate plane, covering rotations, translations, reflections, and dilations. Each shape's transformation is analyzed step by step, suitable for students in Grades 8-10.

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