Question: A rectangle has vertices at P(1, 2), Q(1, 6), R(5, 6), and S(5, 2). The rectangle is translated using the rule $ (x, y) \to (x + 5, y + 2) $. What are the coordinates of the image of vertex Q?
1. **State the problem:** We have a rectangle with vertex $Q$ at coordinates $ (1, 6) $. We apply the translation rule $ (x, y) \to (x + 5, y + 2) $ to find the new coordinates of $Q$.
2. **Formula for translation:** The translation rule means we add $5$ to the $x$-coordinate and $2$ to the $y$-coordinate of each point.
3. **Apply the translation to $Q$:**
$$
Q' = (1 + 5, 6 + 2) = (6, 8)
$$
4. **Interpretation:** The image of vertex $Q$ after translation is at $ (6, 8) $.
5. **Answer:** The correct choice is $ (6, 8) $.