Question

which composition of transformations maps figure efgh to figure efgh?
a reflection across line k followed by a translation down
a translation down followed by a reflection across line k
a 180° rotation about point g followed by a translation to the right
a translation to the right followed by a 180° rotation about point g

Explanation:

Step1: Observe reflection

Figure EFGH is reflected across line k to get an intermediate - figure E'F'G'H' (same orientation as EFGH but on the other side of k).

Step2: Observe translation

The intermediate - figure E'F'G'H' is then translated down to get E''F''G''H''.

Step3: Analyze other options

For the translation - first options, the orientation and position won't match. For rotation - based options, the rotation about point G and subsequent translations won't result in the correct figure E''F''G''H''.

Answer:

A. a reflection across line k followed by a translation down