Question

select the correct answer.

triangle \\(abc\\) is reflected across the y-axis and then dilated by a factor of \\(\frac{1}{2}\\) centered at the origin. which statement correctly describes the resulting image, triangle \\(def\\)?

• both the reflection and dilation preserve the side lengths and angles of triangle \\(abc\\).
• the dilation preserves the side lengths and angles of triangle \\(abc\\). the reflection does not preserve side lengths and angles.
• the reflection preserves the side lengths and angles of triangle \\(abc\\). the dilation preserves angles but not side lengths.
• neither the reflection nor the dilation preserves the side lengths and angles of triangle \\(abc\\).

Explanation:

Analyze the properties of reflection

Using the Reflections in the Coordinate Plane and Geometric Transformations knowledge points

$$
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Analyze the properties of dilation

Using the Geometric Transformations knowledge point

$$
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Evaluate the given statements

Using the Geometric Transformations knowledge point

$$
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Answer:

• Both the reflection and dilation preserve the side lengths and angles of triangle ABC.
• The dilation preserves the side lengths and angles of triangle ABC. The reflection does not preserve side lengths and angles.
• The reflection preserves the side lengths and angles of triangle ABC. The dilation preserves angles but not side lengths. (Correct answer)
• Neither the reflection nor the dilation preserves the side lengths and angles of triangle ABC.