Geometry

Question Analysis:
This problem involves reversing a glide reflection. You are given the final image (Q′), the reflection line (y = 4), and the translation vector (2, 0), and your task is to determine the original point Q.
The main focus is on reversing both the translation and reflection, in the correct order, considering that the translation vector moves the point horizontally.

Key Concept Explanation:
A glide reflection consists of:
Reflection over a line (in this case, the line is y = 4).
A translation parallel to that line (in this case, the vector is (2, 0), meaning the translation is horizontal).
To reverse the glide reflection:
Undo the translation (subtract the translation vector).
Then undo the reflection (reflect back over the same mirror line).

Step-by-Step Solution:
Given data:
Final point Q′ = (10, 6)
Reflection line: y = 4
Translation vector: (2, 0)
Step 1: Undo the translation.
The translation vector is (2, 0), so to undo the translation, subtract the vector from Q′:
Q = (10 – 2, 6 – 0) = (8, 6)
Step 2: Undo the reflection.
The point Q′(8, 6) is reflected across the line y = 4. To reverse the reflection:
The point Q′(8, 6) is 2 units above the reflection line y = 4.
Therefore, to reverse the reflection, the original point must be 2 units below the line y = 4.
This gives the y-coordinate of Q as 2.
So, the original point Q is (8, 2).

Option Analysis:
A) (10, 2) → ✖ Incorrect: This point doesn’t account for the correct reverse transforma...