Question

which transformation shows a reflection of (\triangle def)?

Explanation:

To determine which transformation shows a reflection of \( \triangle DEF \), we recall that a reflection (or flip) is a transformation that creates a mirror image of the original figure across a line (the line of reflection). The key properties of a reflection are:

1. Distance Preservation: Corresponding points (e.g., \( D \) and \( D' \), \( E \) and \( E' \), \( F \) and \( F' \)) are equidistant from the line of reflection.
2. Mirror Image: The reflected figure is a mirror image of the original, with the line of reflection acting as the "mirror."

Analyzing the Options (Visually):

• First Figure (Green \( \triangle DEF \), Light Blue \( \triangle D'E'F' \)):

The orientation and position suggest a rotation or translation, not a reflection. The sides and angles do not align as a mirror image.

• Second Figure (Purple \( \triangle DEF \), Light Purple \( \triangle D'E'F' \)):

The light purple triangle appears to be a mirror image of the purple triangle across a vertical or horizontal line. Corresponding sides (marked with tick marks) are symmetric, and the orientation is reversed (consistent with a reflection).

• Third Figure (Blue \( \triangle DEF \), Light Blue \( \triangle D'E'F' \)):

This looks like a translation (slide) or rotation, as the orientation and position do not show the mirror - like symmetry of a reflection.

A reflection creates a mirror - image of a figure across a line. The second transformation (with the purple \( \triangle DEF \) and light purple \( \triangle D'E'F' \)) shows the mirror - image property: corresponding points are equidistant from the line of reflection, and the figure is reversed in orientation (consistent with a reflection). The other two transformations show rotation or translation, not reflection.

Answer:

The transformation with the purple \( \triangle DEF \) and the light purple \( \triangle D'E'F' \) (the middle option) shows a reflection of \( \triangle DEF \).