Determine a series of transformations that would map Figure X onto Figure Y.
Understand the Problem
The question asks to identify the series of transformations (reflection, translation, rotation, dilation) that would map Figure X onto Figure Y. This involves understanding how the position and orientation of Figure X changes to become Figure Y.
Answer
A reflection over the x-axis followed by a translation 7 unit(s).
Answer for screen readers
A reflection over the x-axis followed by a translation 7 unit(s).
Steps to Solve
- Identify the Reflection
Figure X is reflected over the x-axis. This can be visualized by imagining folding the graph along the x-axis; Figure X would then be on the same side as Figure Y but not overlapping.
- Identify the Translation
After the reflection, Figure X needs to be moved (translated) downward to overlap with Figure Y. Count the number of units it needs to be translated. Corresponding points on Figure X and Figure Y will help determine this distance. If we consider the top point on Figure X, we reflect it over the x-axis (from y = 9 to y = -9). We then translate to the corresponding top point of Figure Y (y = -2). The distance of translation is $9 - 2 = 7$ units downwards.
- Specify the Translation Direction
Since the translation moves the figure downwards, it's a translation in the negative y-direction.
A reflection over the x-axis followed by a translation 7 unit(s).
More Information
Transformations are a crucial part of geometry, helping us understand how figures can be manipulated in space. Reflections create mirror images, while translations simply shift figures without changing their orientation.
Tips
A common mistake is to confuse the order of transformations or miscount the units of translation. Another mistake could be to incorrectly identify the axis of reflection.
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