Question

Figure 2 is a transformation of Figure 1, and vertex X is on line n.

Figure 1 and figure 2 are irregular pentagons shown side by side. Figure 1 is smaller than Figure 2 and is oriented in a direct that is opposite of Figure 2. A dotted line labeled line n is shown between Figure 1 and Figure 2, with vertex X being a shared vertex of both figures.

Which sequence of transformations could Figure 1 have undergone to result in Figure 2?


a rotation of
180
°
counterclockwise about vertex X followed by a dilation through vertex X by scale factor less than 1


a reflection over line n followed by a dilation through vertex X by scale factor greater than 1


a rotation of
180
°
counterclockwise about vertex X followed by a dilation through vertex X by scale factor greater than 1


a reflection over line n followed by a dilation through vertex X by scale factor less than 1

Answer 1

Answer: reflection over line n followed by a dilation through vertex X by scale factor greater than 1.

Reason: Figure 2 is an enlargement of Figure 1 (so scale factor >1) and has reversed orientation (so a reflection is required). Reflecting across line n fixes X (on the axis) and then dilating about X enlarges the reflected image to match Figure 2.