To determine a series of transformations that Lyndsey can use to move the old figure to the new figure and to explain why the figures are similar, let's outline the steps commonly used in geometric transformations.
-
Identify the Transformations: The common transformations that can be applied to a geometric figure include:
- Translation: Moving the figure without rotating or resizing it.
- Rotation: Turning the figure around a point.
- Reflection: Flipping the figure over a line.
- Scaling: Resizing the figure while maintaining its shape.
-
Series of Transformations: Assuming that Lyndsey's original figure and the new figure need to maintain similarity, here is a potential series of transformations:
- Translation: Move the old figure (in terms of coordinates) horizontally and/or vertically to align it with a corresponding point of the new figure.
- Depending on the specific positioning of the figures, additional transformations might include:
- Rotation: If the new figure is oriented differently, a rotation around the center or a specific point could be necessary.
- Reflection: If the new figure is mirrored compared to the old one, a reflection over a specific axis may also be required.
-
Explanation of Similarity: The figures are considered similar if:
- They have the same shape but are different in size, meaning that corresponding angles are equal, and the lengths of corresponding sides are proportional.
- The transformations applied do not alter the angles but only reposition, rotate, or resize, thus preserving the ratio of the sides.
Therefore, if Lyndsey accurately applies these transformations to the old figure (starting with translation, followed potentially by rotation and/or reflection), she can successfully convert it into the new figure, while ensuring that both figures bear proportional relationships among their sides and equal measures for corresponding angles, thus confirming their similarity.
Final Steps
After determining the specific transformations needed (translation, possible rotation, or reflection), Lyndsey should:
- Confirm the corresponding points match after each transformation.
- Check that the angles remain constant and that the sides maintain their proportional relationships.
In summary, by applying appropriate transformations, Lyndsey will ensure that the original figure transforms into a similar figure that is consistent in shape and proportional across its dimensions.