Question

A transformation of ADEF results in AD'EF.

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.

Answer 1

The transformation is a rotation.

Explanation:

The sides of the pre-image are congruent (≅) to the corresponding sides of the image. Therefore this was not a dilation. Since the direction of the shape was changed it is not a transformation. Additionally, even if a line were drawn equidistant from both triangles the shapes would not align to make the fact that this was a reflection true. Therefore it is a rotation.

What are transformations?

Transformations include:

• translations (no change in size or direction, just moved to a different spot)
• dilations (change in size)
• reflections (no change in size however the new image is a mirror view of the pre-image)
• rotations (no change in size or position, however the shaped was turned to face a new direction)

Answer 2

The transformation is a rotation.

Explanation:

Corresponding sides of the image and pre-image are marked congruent, so there is no dilation involved. Dilation changes the lengths of corresponding segments.

The vertex order DEF is clockwise in both the image and pre-image, so there is no reflection involved. (Reflection reverses the vertex order to counterclockwise.)

Segment FD points to the northeast, but segment F'D' points to the west, so a rotation is involved.

With no coordinate axes, we cannot tell if translation is involved or not. (We presume some translation is required, but the primary transformation of interest here is the rotation.)