Pregunta
WRITE Which properties of a figure are preserved under a rotation from the preimage to the image? Explain.
Select all that apply.
A) Angle measures are preserved because angle measures remain the same measure.
B) Parallelism is preserved because parallel lines remain parallel.
C) Position is preserved because the image and the preimage are congruent.
D) Distance is preserved because the lengths of segments remain the same measure.
E) Collinearity is preserved because points remain on the same lines.
Select all that apply.
A) Angle measures are preserved because angle measures remain the same measure.
B) Parallelism is preserved because parallel lines remain parallel.
C) Position is preserved because the image and the preimage are congruent.
D) Distance is preserved because the lengths of segments remain the same measure.
E) Collinearity is preserved because points remain on the same lines.
Ask by Ramos Hampton. in the United States
Nov 20,2024
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The properties preserved under rotation are: angle measures, parallelism, distance, and collinearity.
Solución
When a figure is rotated, several properties are preserved from the preimage to the image. The correct options that apply are:
A) Angle measures are preserved because angle measures remain the same measure.
This is true; the angles in the figure maintain their measures after rotation.
This is true; the angles in the figure maintain their measures after rotation.
B) Parallelism is preserved because parallel lines remain parallel.
This is also true; if two lines are parallel in the preimage, they will remain parallel in the image after rotation.
This is also true; if two lines are parallel in the preimage, they will remain parallel in the image after rotation.
C) Position is preserved because the image and the preimage are congruent.
This statement is somewhat misleading. While the figures are congruent, the specific position of the figure in the plane may change due to the rotation. Therefore, this option is not correct.
This statement is somewhat misleading. While the figures are congruent, the specific position of the figure in the plane may change due to the rotation. Therefore, this option is not correct.
D) Distance is preserved because the lengths of segments remain the same measure.
This is true; the distances between points (lengths of segments) do not change after rotation.
This is true; the distances between points (lengths of segments) do not change after rotation.
E) Collinearity is preserved because points remain on the same lines.
This is true; if points are collinear in the preimage, they will remain collinear in the image after rotation.
This is true; if points are collinear in the preimage, they will remain collinear in the image after rotation.
In summary, the properties preserved under rotation are:
- A) Angle measures
- B) Parallelism
- D) Distance
- E) Collinearity
So, the correct selections are A, B, D, and E.
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Simplifique esta solución The Deep Dive
When a figure is rotated, several properties remain unchanged, giving rise to some fun geometric facts! First off, angle measures are absolutely preserved; every angle maintains its original measurement despite the twist and turn. Next up, you can take a look at lines: parallel lines stay parallel after the rotation, maintaining that cool vibe of being side-by-side no matter how you spin it!
Additionally, another nifty property is that distance stays the same; the lengths of segments don’t get stretched or squished, they’re just as long as they were before the rotation. All those points? They just shift around, but they stay on the same lines, proving that collinearity is also preserved during the rotation dance!
So, to sum it up, the correct answers include A, B, D, and E! Each of these properties shows just how magical and consistent geometry can be, even when it’s doing a little pirouette.
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