Geometry

Question Analysis:
This question involves reversing a glide reflection.
The final image point P′ is given, and you are provided with the reflection line and the translation vector.
The challenge is to determine the original coordinates of point P before the glide reflection.
The main focus is on understanding the inverse process: undoing the translation first, then undoing the reflection across a vertical line.

Key Concept Explanation:
A glide reflection is a combination of:
A reflection over a line (in this case, the vertical line x = 3),
Followed by a translation parallel to that line (in this case, vertical translation by the vector (0, 3)).
To find the pre-image, we reverse this process:
Undo the translation (subtract the translation vector from the image point).
Undo the reflection (reflect back over the same mirror line).

Step-by-Step Solution:
Given:
P′ = (6, 5)
Reflection line: x = 3 (vertical line)
Translation vector: (0, 3)
Step 1: Undo the translation.
Since the translation was (0, 3), subtract that from P′:
(6, 5) – (0, 3) = (6, 2)
Now, this point (6, 2) is the image after reflection but before the translation.
Step 2: Undo the reflection.
Reflect the point (6, 2) over the line x = 3:
The point is 3 units to the right of x = 3.
Reflecting it over x = 3 moves it 3 units to the left of the line:
x = 3 – 3 = 0
So, the original point P = (0, 2)

Option Analysis:
A) (9...