To determine the series of transformations that would map Figure $Y$ onto Figure $Z$, let's analyze the image step by step:

1. Figure $Y$ is located in the fourth quadrant.
2. Figure $Z$ is located in the second quadrant.
3. Both figures seem to be similar in shape and size, but their orientation and position are different.

Transformations to Map $Y$ to $Z$:

1. Reflection:

   • Reflect Figure $Y$ over the x-axis to bring it into the upper half of the coordinate plane. After reflecting over the x-axis, the figure should lie in the first quadrant.

2. Translation:

   • Translate the reflected figure upwards and to the left to move it from its current position in the first quadrant to the second quadrant, where Figure $Z$ is located.

Thus, the transformation sequence is likely:

• Reflect across the x-axis followed by a translation (up and to the left).

Let me know if you would like any further details or clarifications!

Here are 5 related questions to expand this concept:

1. What is the general formula for reflecting a point across the x-axis?
2. How do you describe a translation in terms of vector notation?
3. What is the result of reflecting a figure across both the x- and y-axes?
4. How can you combine transformations like rotations and reflections to achieve a desired mapping?
5. Can a rotation be used instead of reflection and translation in this scenario?

Tip: Always check if a reflection changes the orientation of a figure, and ensure you account for any translations needed to match positions exactly.