Question

Figure ABCD is transformed to figure A prime B prime C prime D prime, as shown below: A coordinate grid is shown from negative 5 to 0 to 5 on both x- and y-axes at increments of 1. A polygon ABCD has A at ordered pair negative 4, 3, B at ordered pair negative 2, 4, C at ordered pair negative 3, 1, D at ordered pair negative 4, 1. A polygon A prime B prime C prime D prime has A prime at ordered pair 4, negative 2, B prime at ordered pair 2, negative 1, C prime at ordered pair 3, negative 4, D prime at ordered pair 4, negative 4. Which of the following sequences of transformations is used to obtain figure A prime B prime C prime D prime from figure ABCD? Reflection over the x-axis followed by a translation to the right by 5 units Reflection over the y-axis followed by a translation down by 5 units Counterclockwise rotation by 180 degrees about the origin followed by a translation to the right by 5 units Counterclockwise rotation by 180 degrees about the origin followed by a translation down by 5 units

Answer 1

Reflection about the y-axis followed by a translation down by 5 units

Answer 2

The transformed figure has the opposite orientation (A'B'C'D' is counterclockwise, whereas ABCD is clockwise), so a reflection is involved. The sgment C'D' is still at the bottom, as is CD, so the reflection must be across a vertical line.

In the attached, the light-blue figure A''B''C''D'' shows the reflection of ABCD across the y-axis. It is easy to see that figure A'B'C'D' is a translation of that 5 units downward.

The appropriate choice is the 2nd one ...

... Reflection over the y-axis followed by a translation down by 5 units.