To determine the correct sequence of transformations that can verify that two figures are similar, we should consider the properties of similar figures. Two figures are similar if one can be obtained from the other through a sequence of transformations that includes dilation (to change size proportionately) and/or reflections, rotations, and translations (to change position or orientation).
In your case, you mention "dilate the unshaded figure by a scale factor of" and then reflect across either the x-axis or y-axis.
-
Dilation changes the size of the figure while maintaining the proportion of the angles and sides, meaning the shape remains the same but changes in scale.
-
Reflection changes the orientation of the figure, but it doesn’t affect the size or shape (keeping proportions intact).
To determine which specific transformations will lead to verifying similarity, you would need to fill in the blank for the scale factor. The value of the scale factor will determine the size relation between the two figures.
You should analyze the options provided:
- Dilate by a scale factor and then reflect across the x-axis or y-axis.
- Both transformations (dilation and reflection) maintain similarity properties.
However, since the options listed all focus on "dilate by a scale factor about the origin" followed by a reflection, and without knowing the specific scale factors or the original and target figures, we can't definitively choose one option over the others without additional data.
In general:
-
If the unshaded figure matches the orientation of the shaded figure after applying either sequence (dilate then reflect), they could be considered similar.
-
If the figures only differ by orientation (and not size), either reflection option could prove similarity post-dilation.
To summarize, you must ensure both the scale factor and the figure's orientation are consistent to conclude if the transformation proves similarity.
2 answers