Final answer:
The best description of the glide reflection is option D: (x, y) → (x-12, y+2) followed by reflection in the y-axis.
Step-by-step explanation:
To determine which transformation best describes the glide reflection that maps point E with coordinates (5, 7) to its image E' with coordinates (-7, 9), we need to consider the necessary translation and reflection components of a glide reflection.
Firstly, look at the translation part. To find the translation, we subtract the original coordinates of E from those of E':
- Translation in the x direction: -7 - 5 = -12
- Translation in the y direction: 9 - 7 = +2
So, point E is translated to (-7, 9) by moving it 12 units left (in the negative x direction) and 2 units up (in the positive y direction).
Next, consider the reflection. Reflection in the x-axis would change the sign of the y-coordinate, but since the y-coordinate has increased from 7 to 9, this cannot be a reflection in the x-axis. A reflection in the y-axis changes the sign of the x-coordinate, which can be consistent with our points; therefore, we suspect a reflection in the y-axis is part of the transformation.
Thus, the best description of the glide reflection is option D): (x, y) → (x-12, y+2) followed by reflection in the y-axis, which means that we first translate the point by -12 in the x direction and +2 in the y direction, and then reflect it in the y-axis.