https://file.aiquickdraw.com/mathbot/file/1728999753170q7tfddqr.jpg

To determine the sequence of transformations that maps the figure \( IJKL \) to \( I'J'K'L' \), let’s analyze the movements step by step:

1. **Observation of the original and final shapes:**
   - \( IJKL \) is located in the third quadrant of the coordinate plane, while \( I'J'K'L' \) is in the first quadrant.
   - The orientation of the two shapes is similar (as the angles between the points are preserved), but the positions have shifted significantly.

2. **Reflection:**
   - The figure appears to have undergone a reflection, likely across a horizontal line because the orientation stays the same but the position changes. The most likely line of reflection is \( y = -3 \), which is in between the two quadrants and reflects points from the third quadrant to the first quadrant.

3. **Rotation:**
   - After the reflection, there seems to be a rotation. The figure needs to be rotated around the origin by 180° to align the orientation of \( IJKL \) with that of \( I'J'K'L' \). This step is necessary to bring the points into their final position.

### Correct answer:
The sequence of transformations that maps \( IJKL \) onto \( I'J'K'L' \) is:
- A reflection across the line \( y = -3 \), followed by a 180° clockwise rotation around the origin.

This matches the first option provided in the image.

Would you like further details or have any questions?

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Here are five related questions:
1. How can you identify the line of reflection in a transformation?
2. What are the effects of rotating a shape by 180° around the origin?
3. Can a figure undergo a reflection without changing its orientation? Why or why not?
4. What other types of transformations preserve the size and shape of a figure?
5. How does reflecting a figure across a vertical line differ from reflecting it across a horizontal line?

**Tip:** Always analyze both the orientation and the position of a figure when determining transformations. This helps in correctly identifying whether a reflection, rotation, or translation is involved.

Which sequence of transformations maps IJKL onto I'J'K'L'?

This problem explores a sequence of transformations that map the shape IJKL to I'J'K'L'. Learn how reflections across a horizontal line and rotations around the origin can be used to solve this geometric transformation problem. Suitable for students in Grades 7-9.

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