Which of the following best determines if the transformation of a figure on a coordinate plane is a reflection?
A.The figures are congruent, the orientation of vertices is the same, and the line of reflection produces an image that has opposite coordinates from the preimage.
B.The figures are similar, the orientation of vertices is the same, and the line of reflection produces an image that slides the image horizontally from the preimage.
C.The figures are congruent, the orientation of vertices is not the same, and the line of reflection maps the same distance from corresponding points.
D.The figures are similar, the orientation of vertices not the same, and the line of reflection maps the same distance from corresponding points.


The correct answer is:

**C. The figures are congruent, the orientation of vertices is not the same, and the line of reflection maps the same distance from corresponding points.**

### Explanation:
- A reflection transformation ensures that the preimage and image are **congruent**, meaning they have the same size and shape.
- Reflections reverse the **orientation** of the figure. This is a key distinguishing feature: the vertices are ordered differently in the image versus the preimage.
- The **line of reflection** is equidistant from corresponding points on the preimage and image. Each point on the preimage is mirrored over the line of reflection.

### Do you want me to provide a detailed breakdown or a coordinate example?

Here are 5 follow-up questions to expand your understanding:
1. How can you determine the line of reflection between two congruent figures?
2. What are some ways to identify if a transformation is a reflection without graphing?
3. How does the orientation of a figure change in other types of transformations, such as rotations or translations?
4. What real-life applications use reflections in their principles?
5. Can a reflection be combined with other transformations to create new effects?

**Tip:** To quickly test if a transformation is a reflection, check for congruence and see if the figure's vertices flip in their clockwise/counterclockwise order.

Which of the following best determines if the transformation of a figure on a coordinate plane is a reflection?
A. The figures are congruent, the orientation of vertices is the same, and the line of reflection produces an image that has opposite coordinates from the preimage.
B. The figures are similar, the orientation of vertices is the same, and the line of reflection produces an image that slides the image horizontally from the preimage.
C. The figures are congruent, the orientation of vertices is not the same, and the line of reflection maps the same distance from corresponding points.
D. The figures are similar, the orientation of vertices not the same, and the line of reflection maps the same distance from corresponding points.

Discover how to determine if a transformation on a coordinate plane is a reflection. Learn about congruence, orientation changes, and the role of the line of reflection in this Grade 8-10 problem. Includes key concepts like distance formula and reflection theorem.

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