To determine the series of transformations that map polygon $ABCDE$ onto polygon $A'B'C'D'E'$, we can observe the following:

Step-by-step analysis:

1. Reflection across the y-axis: The original polygon $ABCDE$ is on the right side of the y-axis (positive x-values), while the target polygon $A'B'C'D'E'$ is on the left side (negative x-values). The first transformation appears to be a reflection over the y-axis.

   This reflection changes the coordinates as follows: $(x, y) \rightarrow (-x, y)$

2. Rotation by 90° counterclockwise: After reflection, the shapes' orientation is still not aligned. To match the orientation of $A'B'C'D'E'$, the next step is a 90° counterclockwise rotation around the origin.

   A 90° counterclockwise rotation changes the coordinates as: $(x, y) \rightarrow (-y, x)$

3. Translation: After the reflection and rotation, the shapes still don't match in position. The final step is a translation to move the reflected and rotated polygon to the correct location on the grid. Observing the coordinates, a translation of 2 units down and 1 unit left (or, $(-1, -2)$) seems appropriate to align the polygons.

Transformation sequence:

1. Reflect across the y-axis: $(x, y) \rightarrow (-x, y)$.
2. Rotate 90° counterclockwise around the origin: $(-x, y) \rightarrow (-y, -x)$.
3. Translate 1 unit left and 2 units down: $(-y, -x) \rightarrow (-y-1, -x-2)$.

Would you like more details on these transformations or have any other questions?

Here are five related questions:

1. What is the general formula for reflecting a point over the y-axis?
2. How would the transformation differ if we rotated by 180° instead of 90°?
3. Can you explain how translation affects both the x and y coordinates?
4. How would a clockwise rotation affect the transformation?
5. Can we describe transformations using matrix operations?

Tip: For composite transformations (like reflections followed by rotations), it helps to visualize or apply each step incrementally to avoid confusion.