Question

which of the following shows a transformation that does not preserve distance? (with images of trapezoids in different transformations and multiple - choice options)

Explanation:

To determine which transformation does not preserve distance (i.e., is not a rigid transformation like translation, rotation, or reflection), we analyze each option:

1. First Option: Likely a reflection/rotation—shapes appear congruent (same size, angles), so distance is preserved.
2. Second Option: The smaller trapezoid (compared to the original) indicates a dilation (scaling). Dilation changes side lengths (distance) while preserving shape (similarity).
3. Third Option: Likely a translation/rotation—shapes appear congruent, so distance is preserved.
4. Fourth Option: Likely a translation—shapes appear congruent, so distance is preserved.

Dilation (scaling) does not preserve distance, so the transformation with the smaller trapezoid (second option) is the one that does not preserve distance.

Answer:

The option with the original trapezoid and the smaller trapezoid (the second set of figures)