Question
Which of the following transformations will produce a figure that is similar?
Responses
A rotationrotation
B dilationdilation
C reflectionreflection
D translation
Responses
A rotationrotation
B dilationdilation
C reflectionreflection
D translation
Answers
Answered by
GPT-4o mini
To determine which transformation results in a figure that is similar, we need to consider the properties of each transformation:
A. **Rotation**: A rotation changes the orientation of a figure, but it does not change its size or shape. Therefore, the figure remains similar to the original.
B. **Dilation**: A dilation changes the size of a figure while maintaining the shape. This transformation creates a similar figure since all corresponding angles remain equal, and the sides are proportional.
C. **Reflection**: A reflection flips a figure over a line, changing its orientation but preserving its size and shape. Thus, it produces a similar figure.
D. **Translation**: A translation moves a figure without changing its orientation, size, or shape. The result is still similar to the original figure.
Considering these points, the transformations that produce a similar figure are:
- A (rotation)
- B (dilation)
- C (reflection)
- D (translation)
However, among these options, the transformation that is most commonly used to define similarity in terms of proportionality and angles is **B (dilation)**.
So, while all of the transformations listed can yield similar figures, if we are looking for a definitive transformation that inherently denotes similarity, **B (dilation)** is the most appropriate choice.
A. **Rotation**: A rotation changes the orientation of a figure, but it does not change its size or shape. Therefore, the figure remains similar to the original.
B. **Dilation**: A dilation changes the size of a figure while maintaining the shape. This transformation creates a similar figure since all corresponding angles remain equal, and the sides are proportional.
C. **Reflection**: A reflection flips a figure over a line, changing its orientation but preserving its size and shape. Thus, it produces a similar figure.
D. **Translation**: A translation moves a figure without changing its orientation, size, or shape. The result is still similar to the original figure.
Considering these points, the transformations that produce a similar figure are:
- A (rotation)
- B (dilation)
- C (reflection)
- D (translation)
However, among these options, the transformation that is most commonly used to define similarity in terms of proportionality and angles is **B (dilation)**.
So, while all of the transformations listed can yield similar figures, if we are looking for a definitive transformation that inherently denotes similarity, **B (dilation)** is the most appropriate choice.