Question
Two transformations are performed on Figure A to produce Figure B. Figure A and Figure B are similar, but not congruent. The first transformation is a reflection over a vertical line.
Question
Which transformation could be the second transformation?
Answer options with 5 options
A.
a reflection over a horizontal line
B.
a translation to the right and down
C.
a 270° counterclockwise rotation about a point on the figure
D.
a dilation with a center at a point on the figure and a scale factor of 1
E.
a dilation with a center at a point not on the figure and a scale factor of 3
Question
Which transformation could be the second transformation?
Answer options with 5 options
A.
a reflection over a horizontal line
B.
a translation to the right and down
C.
a 270° counterclockwise rotation about a point on the figure
D.
a dilation with a center at a point on the figure and a scale factor of 1
E.
a dilation with a center at a point not on the figure and a scale factor of 3
Answers
Answered by
GPT-4o mini
To determine which transformation could be the second transformation after reflecting Figure A to produce Figure B, we need to consider the properties of the transformations involved.
Since Figure A and Figure B are similar but not congruent, the second transformation must change the size of Figure A after it has been reflected. Dilation is a transformation that changes the size of a figure while maintaining its shape, which aligns with the similarity condition.
Let's evaluate the options:
A. **A reflection over a horizontal line** - This would create a figure that is congruent to the previously reflected figure, preserving the size.
B. **A translation to the right and down** - This transformation would not change the size of Figure A; it would simply move it, resulting in congruent figures.
C. **A 270° counterclockwise rotation about a point on the figure** - This would also create a congruent figure due to the preservation of size through rotation.
D. **A dilation with a center at a point on the figure and a scale factor of 1** - This would maintain the original size (no change in size), resulting in a congruent figure.
E. **A dilation with a center at a point not on the figure and a scale factor of 3** - This would increase the size of the figure, creating a similar figure that is larger.
Given these evaluations:
The only option that fulfills the requirement of resulting in a similar (but not congruent) figure through a size change is:
**E. a dilation with a center at a point not on the figure and a scale factor of 3.**
Since Figure A and Figure B are similar but not congruent, the second transformation must change the size of Figure A after it has been reflected. Dilation is a transformation that changes the size of a figure while maintaining its shape, which aligns with the similarity condition.
Let's evaluate the options:
A. **A reflection over a horizontal line** - This would create a figure that is congruent to the previously reflected figure, preserving the size.
B. **A translation to the right and down** - This transformation would not change the size of Figure A; it would simply move it, resulting in congruent figures.
C. **A 270° counterclockwise rotation about a point on the figure** - This would also create a congruent figure due to the preservation of size through rotation.
D. **A dilation with a center at a point on the figure and a scale factor of 1** - This would maintain the original size (no change in size), resulting in a congruent figure.
E. **A dilation with a center at a point not on the figure and a scale factor of 3** - This would increase the size of the figure, creating a similar figure that is larger.
Given these evaluations:
The only option that fulfills the requirement of resulting in a similar (but not congruent) figure through a size change is:
**E. a dilation with a center at a point not on the figure and a scale factor of 3.**