What is a transformation that would not map figure A onto figure A'? 

A transformation that does **not map figure A onto figure A'** is one that alters the shape, size, or orientation of the original figure in such a way that it does not coincide with the target figure. Examples of such transformations include:

1. **Non-Rigid Transformations**: These are transformations that change the size or shape of the figure, such as a **dilation** (scaling) where the figure is either enlarged or reduced. Dilation changes the size of the figure and does not necessarily map figure A onto figure A' if the scaling factor is different from 1.

2. **Incorrect Rotations**: If a figure is rotated by an angle that is not aligned with the required rotation to map A onto A', it will not coincide with A'. For example, if a 90-degree rotation is required, but a 45-degree rotation is applied instead, the figures will not match.

3. **Incorrect Reflections**: If a reflection is done over the wrong axis or line, the resulting figure will not map onto A'. For example, reflecting across the y-axis instead of the x-axis could result in a different orientation.

4. **Translations in the Wrong Direction**: If a translation moves a figure in a different direction or distance than required to map figure A onto A', the figures will not coincide.

5. **Shearing**: A shear transformation shifts the points in a figure in a direction parallel to a given axis, which distorts the shape and therefore will not map figure A onto figure A' unless A' is also a sheared version of A.

If you have any specific figures or examples in mind, please provide them, and I can analyze the scenario in detail.

Would you like more details about any specific type of transformation? Here are some related questions that could help expand your understanding:

1. What are the main types of geometric transformations?
2. How does a reflection differ from a rotation in geometry?
3. What is an example of a transformation that does map a figure onto itself?
4. How can dilation affect the congruence of two figures?
5. How can you determine the transformation needed to map one figure onto another?

**Tip:** Always consider the properties (size, shape, orientation) of the original and resulting figures when determining the type of transformation needed.

What is a transformation that would not map figure A onto figure A'?

Explore different types of geometric transformations, such as dilation, incorrect rotations, reflections, translations, and shearing, that would not map figure A onto figure A'. Learn the properties and effects of these transformations, including size, shape, and orientation changes. Suitable for students in Grades 8-10.

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