Question

a transformation of \\( \triangle def \\) results in \\( \triangle def \\).
which transformation maps the pre - image to the
image?
the transformation is a dilation.
the transformation is a reflection.
the transformation is a rotation.
the transformation is a translation.

Explanation:

• Dilation: Changes the size of a figure. But the two triangles (pre - image \(\triangle DEF\) and image \(\triangle D'E'F'\)) seem to be of the same size (as indicated by the equal - length markings), so it's not a dilation.
• Reflection: Flips a figure over a line. There is no indication of a line of reflection in the problem description and the orientation of the triangles (in terms of the order of vertices) does not suggest a flip.
• Rotation: Turns a figure around a point. There is no indication of a center of rotation in the problem description.
• Translation: Slides a figure without rotating or resizing. Since the triangles are congruent (same size and shape) and the orientation of the vertices (e.g., the order of \(D, E, F\) and \(D', E', F'\) in terms of the markings) is the same (just moved to a new position), it is a translation.

Answer:

The transformation is a translation.