Geometry

Question Analysis:
This question involves geometric transformations.
The main focus is on understanding which transformations preserve congruence (i.e., are isometries).

Key Concept Explanation:
An isometry is a transformation that preserves distance and angle measures — meaning the pre-image and image are congruent.
The main types of isometries are:
Translation
Rotation
Reflection
A dilation, however, does not preserve size unless the scale factor is 1 — so it is not an isometry when the scale factor is anything other than 1.

Step-by-Step Solution:
Check each transformation to see if it preserves congruence:
A. Reflection: Flips the shape, but keeps size and angles — ✅ Isometry
B. Rotation: Turns the shape around a point, size remains the same — ✅ Isometry
C. Dilation (scale factor of 2): Changes the size, not just the position — ❌ Not an isometry
D. Translation: Moves shape without changing size — ✅ Isometry
Conclusion:
The only transformation listed that does not preserve congruence is C. Dilation with a scale factor of 2.

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