Question

select all the correct answers.

which two transformations preserve the side lengths and angles of the preimage?

• a reflection across line m
• a translation to the right
• a stretch by a factor of 4
• a dilation by a factor of 4

Explanation:

Define rigid transformations

Using the Rigid Transformations knowledge point

• Rigid transformations (isometries) preserve both distance (side lengths) and angle measures.
• Preimage and image remain congruent.

Analyze each option

Using the Rigid Transformations knowledge point

• Reflection across line m: A reflection is a rigid transformation. It preserves side lengths and angles.
• Translation to the right: A translation is a rigid transformation. It preserves side lengths and angles.
• Stretch by a factor of 4: A stretch changes side lengths, so it is not a rigid transformation.
• Dilation by a factor of 4: A dilation changes side lengths (scaling them by 4), so it is not a rigid transformation.

Select the correct answers

Using the Rigid Transformations knowledge point

• The two transformations that preserve side lengths and angles are the reflection and the translation.

Answer:

• a reflection across line m (Correct answer)
• a translation to the right (Correct answer)
• a stretch by a factor of 4
• a dilation by a factor of 4