What reflection of the parallelogram ABCD results in the image A’B’C’D’? Use pencil and paper. Is the image unique using one reflection? Is the image unique using one reflection and one translation?
Reflect ABCD across the line =
What reflection of the parallelogram ABCD results in the image A’B’C’D’? Use pencil and paper. Is the image unique using one reflection? Is the image unique using one reflection and one translation? Reflect ABCD across the line =
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To determine the reflection of parallelogram ABCD that results in image A’B’C’D’, we first need to identify the line of reflection. The line of reflection must be the perpendicular bisector of the segments connecting corresponding points (e.g., A to A’, B to B’, etc.) in ABCD and A’B’C’D’.
1. Finding the Line of Reflection:
– Sketch both the original parallelogram ABCD and the resulting image A’B’C’D’.
– Draw the midpoints of segments AA’, BB’, CC’, and DD’.
– The line of reflection will pass through these midpoints and will be perpendicular to the segments connecting corresponding points.
2. Uniqueness of Image:
– The image created by a single reflection is not necessarily unique, meaning that more than one line of reflection can produce the same image.
– For example, if the parallelogram is symmetric, you can have multiple lines of reflection resulting in the same transformed image.
3. Using One Reflection and One Translation:
– If you apply one reflection followed by a translation, you can effectively achieve different placements of the image while maintaining its shape and orientation. This means the image can also be non-unique in this context.
To summarize:
– The specific line of reflection for ABCD to A’B’C’D’ can be determined by identifying midpoints and ensuring it’s perpendicular.
– The image is not unique under one reflection