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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?

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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.

Determine a series of transformations that would map polygon ABCDE onto polygon A'B'C'D'E'.

This problem involves determining a series of transformations, including reflection over the y-axis, 90° counterclockwise rotation, and translation, to map polygon ABCDE onto polygon A'B'C'D'E'. Detailed step-by-step instructions are provided.

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