https://file.aiquickdraw.com/mathbot/file/1727289344155eg43bh8y.jpg

To map Figure Y onto Figure Z, we can use a combination of transformations: reflection, rotation, and translation.

### Steps:
1. **Reflection**:
   - Reflect Figure Y over the x-axis. This will flip the figure from the third quadrant to the first quadrant. After reflection, the orientation of the figure will match Figure Z but in a different position.

2. **Rotation**:
   - Rotate the reflected Figure Y 90° counterclockwise about the origin. This will rotate the triangle into the same orientation as Figure Z.

3. **Translation**:
   - Finally, translate the rotated figure so that it aligns with Figure Z. This involves moving the figure to the left and up to match the position of Figure Z.

### Transformation Summary:
1. **Reflect** Figure Y across the x-axis.
2. **Rotate** the reflected figure 90° counterclockwise about the origin.
3. **Translate** the figure to the coordinates that match Figure Z.

Would you like any further explanation on these steps or how they apply specifically to the coordinates of the shapes?

Here are 5 related questions to deepen your understanding:
1. How do you find the line of reflection between two figures?
2. What are the properties of a 90° counterclockwise rotation?
3. How can you calculate the translation vector required to move one figure onto another?
4. What is the general rule for reflecting points over the x-axis?
5. How do different transformations affect the orientation and size of a figure?

**Tip:** Always perform transformations in small steps, verifying the result after each transformation.

Determine a series of transformations that would map Figure Y onto Figure Z.

Explore the steps to map Figure Y onto Figure Z using reflection, rotation, and translation. This problem helps students understand key concepts in transformations and coordinate geometry, suitable for Grades 8-10.

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